ALBERT

Beschreibung / Inhaltsverzeichnis: Contents --- Foreword --- Chapter 1: Introduction and Overview --- Chapter 2: The Three Phases of Global Liquidity --- 2.1: Conceptual and Measurement Issues --- 2.2: First Phase of Global Liquidity --- 2.2.1: Round-trip Bank Flows to the US --- 2.2.2: Banking Sector Flows to the Rest of the World --- 2.2.3: Exchange Rates and Leverage --- 2.3: Second Phase of Global Liquidity --- 2.4: The Case of Emerging Asia --- 2.5: Third Phase and Onward --- 2.6: References --- Chapter 3: Early Warning Indicators for Financial Vulnerabilities --- 3.1: Principles for Selection of Early Warning Indicators --- 3.2: Core and Noncore Liabilities --- 3.3: References --- Chapter 4: Emerging Asia’s Noncore Liabilities and Policy Effectiveness --- 4.1: Bank-led Flows, Noncore Liabilities, and Credit Growth --- 4.2: Reassessing Monetary Policy --- 4.3: Appendix --- 4.4: References --- Chapter 5: Capital Flows and Income Distribution --- 5.1: National Policy Remains Key --- 5.2: How Capital Flows Affect Income Inequality --- 5.3: Prioritization for a Multi-Objective Goal --- 5.4: Appendix --- 5.5: References --- Chapter 6: Policy Implications --- 6.1 Tailoring Policies to Vulnerabilities --- 6.2 Macroprudential Tools --- 6.2.1 Bank Capital-Oriented Tools --- 6.2.1.1 Capital Requirements that Adjust Over the Cycle --- 6.2.1.2 Forward-Looking Provisioning --- 6.2.1.3: Leverage caps --- 6.2.1.4: Loan-To-Value and Debt-Service-To-Income Caps --- 6.2.1.5: Loan-to-Deposit caps --- 6.2.1.6: Levy on Noncore Liabilities --- 6.2.1.7: Unremunerated Reserve Requirements --- 6.2.2: Relative Merits of URR versus Levies/Taxes --- 6.2.3: Relationship with other Stabilization Policies --- 6.3: Financial Integration and Institutional Design --- 6.4: Policy Choices --- 6.5: References

Beschreibung / Inhaltsverzeichnis: Wetlands and Water Framework Directive: protection, management and climate change --- Synergies and Conflicts between Water Framework Directive and Natura 2000: Legal requirements, technical guidance and experiences from practice --- Can Natura 2000 Sites Benefit from River Basin Management Planning Under a Changing Climate? Lessons from Germany --- Do water management and climate-adapted management of wetlands interfere in practice? Lessons from the Biebrza Valley, Poland --- Wetlands in river valleys as an effect of fluvial processes and anthropopression --- New vision of the role of land reclamation systems in nature protection and water management

Beschreibung / Inhaltsverzeichnis: Introduction: concept of TAIGA --- Geochemical constraints on potential biomass sustained by subseafloor water-rock interactions --- Microbial cell densities, community structures, and growth in the hydrothermal plumes of subduction hydrothermal systems --- Systematics of distributions of various elements between ferromanganese oxides and seawater from natural observation, thermodynamics, and structures --- Evaluating hydrothermal system evolution using geochronological dating and biological diversity analyses --- Quantification of microbial communities in hydrothermal vent habitats of the Southern Mariana Trough and the Mid-Okinawa Trough --- Development of hydrothermal and frictional experimental systems to simulate sub-seafloor water–rock–microbe interactions --- Experimental hydrogen production in hydrothermal and fault systems: Significance for habitability of subseafloor H2 chemoautotroph microbial ecosystems --- Experimental assessment of microbial effects on chemical interaction between seafloor massive sulfides and seawater at 4℃ --- A compilation of the stable isotopic compositions of carbon, nitrogen, and sulfur in soft body parts of animals collected from deep-sea hydrothermal vent and methane seep fields: variations in energy source and importance of subsurface microbial processes in the sediment-hosted systems --- Tectonic background of four hydrothermal fields along the Central Indian Ridge --- Indian Ocean hydrothermal systems: seafloor hydrothermal activities, physical and chemical characteristics of hydrothermal fluids, and vent-associated biological communities --- Petrology and geochemistry of mid-ocean ridge basalts from the southern Central Indian Ridge --- Petrology of peridotites and related gabbroic rocks around the Kairei-hydrothermal field in the Central Indian Ridge --- Distribution and Biogeochemical Properties of Hydrothermal Plumes in the Rodriguez Triple Junction --- Vent fauna in the Central Indian Ridge --- The mantle dynamics, the crustal formation, and the hydrothermal activity of the Southern Mariana Trough back-arc Basin --- Seismic structure and seismicity in the Southern Mariana Trough and their relation to hydrothermal activity --- Electrical resistivity structure of the Snail site at the Southern Mariana Trough spreading center --- Asymmetric seafloor spreading of the southern Mariana Trough back-arc basin --- Geochemical characteristics of active backarc basin volcanisms at the southern end of Mariana Trough --- Mineralogical and geochemical characteristics of hydrothermal minerals collected from hydrothermal vent fields in the Southern Mariana spreading center --- Dating of hydrothermal mineralization in active hydrothermal fields in the Southern Mariana Trough --- Intra-field variation of prokaryotic communities on and below the seafloor in the back-arc hydrothermal system of the Southern Mariana Trough --- Vent fauna in the Mariana Trough --- Population history of a hydrothermal vent-endemic snail Alviniconcha hessleri in the Mariana Trough --- Hydrothermal activity in the Okinawa Trough backarc basin -geological background and hydrothermal mineralization- --- Active rifting structures in Iheya Graben and adjacent area of the mid-Okinawa Trough observed through seismic reflection surveys --- ESR dating of barite in sea-floor hydrothermal sulfide deposits in the Okinawa Trough --- Fluid geochemistry of high-temperature hydrothermal fields in the Okinawa Trough --- Sediment‒pore water system associated with native sulfur formation at Jade hydrothermal field in Okinawa Trough --- Comparative investigation of microbial communities associated with hydrothermal activities in the Okinawa Trough --- In situ determination of bacterial growth in mixing zone of hydrothermal vent field on the Hatoma Knoll, Southern Okinawa Trough --- Vent Fauna in the Okinawa Trough --- Brief report of side-scan sonar observations around the Yokoniwa NTO massif --- Examination of volcanic activity: AUV and submersible observations of fine-scale lava flow distributions along the Southern Mariana Trough spreading axis --- Brief report of side-scan sonar imagery observations of the Archaean, Pika, and Urashima hydrothermal sites --- The Yoron Hole: the shallowest hydrothermal site in the Okinawa Trough --- The Irabu Knoll: Hydrothermal site at the eastern edge of the Yaeyama Graben --- Tarama Knoll: Geochemical and biological profiles of hydrothermal activity --- Petrography and geochemistry of basement rocks drilled from Snail, Yamanaka, Archean, and Pika hydrothermal fields at the Southern Mariana Trough by Benthic Multi-coring System (BMS) --- Pore fluid chemistry beneath active hydrothermal fields in the mid-Okinawa Trough: Results of shallow drilling by BMS during TAIGA11 cruise --- The characteristics of the seafloor massive sulfide deposits at the Hakurei Site in the Izena Hole, the Middle Okinawa Trough --- Occurrence of hydrothermal alteration minerals at the Jade hydrothermal field, in the Izena Hole, mid-Okinawa Trough --- Geochemistry of hydrothermal fluids collected from active hydrothermal systems in the southern Mariana Trough backarc spreading center --- Gamma ray doses in water around sea floor hydrothermal area in South Mariana --- 226Ra-210Pb and 228Ra-228Th dating of barite in submarine hydrothermal sulfide deposits collected at Okinawa Trough and South Mariana Trough --- OSL dating of sea floor sediments at the Okinawa Trough --- Immediate change of radiation doses from hydrothermal deposits --- Periodic behavior of deep sea current in the Hatoma Knoll hydrothermal system --- The gelatinous macroplankton community at the Hatoma Knoll hydrothermal vent

Beschreibung / Inhaltsverzeichnis: 1. Supershear Earthquake Ruptures --- Theory, Methods, Laboratory Experiments and Fault Superhighways: An Update.- 2. Civil Protection Achievements and Critical Issues in Seismology and Earthquake Engineering Research.- 3. Earthquake Risk Assessment: Certitudes, Fallacies, Uncertainties and the Quest for Soundness.- 4. Variability and Uncertainty in Empirical Ground-Motion Prediction for Probabilistic Hazard and Risk Analyses.- 5. Seismic Code Developments for Steel and Composite Structures.- 6. Seismic Analyses and Design of  Foundation Soil Structure Interaction.- 7. Performance-based Seismic Design and Assessment of Bridges.- 8. An Algorithm to Justify the Design of Single Story Precast Structures.- 9. Developments in Seismic Design of Tall Buildings: Preliminary Design of Coupled Core Wall Systems --- 10. Seismic Response of  Underground Lifeline Systems.- 11. Seismic Performance of Historical Masonry Structures Through Pushover and Nonlinear Dynamic Analyses.- 12. Developments in Ground Motion Predictive Models and Accelerometric Data Archiving in the Broader European Region --- 13. Towards the “Ultimate Earthquake-proof” Building: Development of an Integrated Low-damage System.- 14. Archive of Historical Earthquake Data for the European-Mediterranean Area --- 15. A Review and Some New Issues on the Theory of  the H/V Technique for Ambient Vibrations.- 16. Macroseismic Intervention Group: The Necessary Field Observation.- 17. Bridging the Gap Between Nonlinear Seismology as Reality and Earthquake Engineering --- 18. The Influence of Earthquake Magnitude on Hazard Related to Induced Seismicity.- 19. On the Origin of Mega-thrust Earthquakes.  

Beschreibung / Inhaltsverzeichnis: Part I Markets, Regulation, and Model Risk --- A Random Holding Period Approach for Liquidity-Inclusive Risk Management --- Regulatory Developments in Risk Management: Restoring Confidence in Internal Models --- Model Risk in Incomplete Markets with Jumps --- Part II Financial Engineering --- Bid-Ask Spread for Exotic Options Under Conic Finance --- Derivative Pricing Under the Possibility of Long Memory in the supOU Stochastic Volatility Model --- A Two-Sided BNS Model for Multicurrency FX Markets --- Modeling the Price of Natural Gas with Temperature and Oil Price as Exogenous Factors --- Copula-Specific Credit Portfolio Modeling --- Implied Recovery Rates—Auctions and Models --- Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence --- Part III Insurance Risk and Asset Management --- Participating Life Insurance Contracts Under Risk Based Solvency Frameworks: How to Increase Capital Efficiency by Product Design --- Reducing Surrender Incentives Through Fee Structure in Variable Annuities --- A Variational Approach for Mean-Variance-Optimal Deterministic Consumption and Investment --- Risk Control in Asset Management: Motives and Concepts --- Worst-Case Scenario Portfolio Optimization Given the Probability of a Crash --- Improving Optimal Terminal Value Replicating Portfolios --- Part IV Computational Methods for Risk Management --- Risk and Computation --- Extreme Value Importance Sampling for Rare Event Risk Measurement --- A Note on the Numerical Evaluation of the Hartman–Watson Density and Distribution Function --- Computation of Copulas by Fourier Methods --- Part V Dependence Modelling --- Goodness-of-fit Tests for Archimedean Copulas in High Dimensions --- Duality in Risk Aggregation --- Some Consequences of the Markov Kernel Perspective of Copulas --- Copula Representations for Invariant Dependence Functions --- Nonparametric Copula Density Estimation Using a Petrov–Galerkin Projection

Beschreibung / Inhaltsverzeichnis: Contents --- Foreword --- Chapter 1: Introduction and Overview --- Chapter 2: The Three Phases of Global Liquidity --- 2.1: Conceptual and Measurement Issues --- 2.2: First Phase of Global Liquidity --- 2.2.1: Round-trip Bank Flows to the US --- 2.2.2: Banking Sector Flows to the Rest of the World --- 2.2.3: Exchange Rates and Leverage --- 2.3: Second Phase of Global Liquidity --- 2.4: The Case of Emerging Asia --- 2.5: Third Phase and Onward --- 2.6: References --- Chapter 3: Early Warning Indicators for Financial Vulnerabilities --- 3.1: Principles for Selection of Early Warning Indicators --- 3.2: Core and Noncore Liabilities --- 3.3: References --- Chapter 4: Emerging Asia’s Noncore Liabilities and Policy Effectiveness --- 4.1: Bank-led Flows, Noncore Liabilities, and Credit Growth --- 4.2: Reassessing Monetary Policy --- 4.3: Appendix --- 4.4: References --- Chapter 5: Capital Flows and Income Distribution --- 5.1: National Policy Remains Key --- 5.2: How Capital Flows Affect Income Inequality --- 5.3: Prioritization for a Multi-Objective Goal --- 5.4: Appendix --- 5.5: References --- Chapter 6: Policy Implications --- 6.1 Tailoring Policies to Vulnerabilities --- 6.2 Macroprudential Tools --- 6.2.1 Bank Capital-Oriented Tools --- 6.2.1.1 Capital Requirements that Adjust Over the Cycle --- 6.2.1.2 Forward-Looking Provisioning --- 6.2.1.3: Leverage caps --- 6.2.1.4: Loan-To-Value and Debt-Service-To-Income Caps --- 6.2.1.5: Loan-to-Deposit caps --- 6.2.1.6: Levy on Noncore Liabilities --- 6.2.1.7: Unremunerated Reserve Requirements --- 6.2.2: Relative Merits of URR versus Levies/Taxes --- 6.2.3: Relationship with other Stabilization Policies --- 6.3: Financial Integration and Institutional Design --- 6.4: Policy Choices --- 6.5: References

Beschreibung / Inhaltsverzeichnis: Part I Markets, Regulation, and Model Risk --- A Random Holding Period Approach for Liquidity-Inclusive Risk Management --- Regulatory Developments in Risk Management: Restoring Confidence in Internal Models --- Model Risk in Incomplete Markets with Jumps --- Part II Financial Engineering --- Bid-Ask Spread for Exotic Options Under Conic Finance --- Derivative Pricing Under the Possibility of Long Memory in the supOU Stochastic Volatility Model --- A Two-Sided BNS Model for Multicurrency FX Markets --- Modeling the Price of Natural Gas with Temperature and Oil Price as Exogenous Factors --- Copula-Specific Credit Portfolio Modeling --- Implied Recovery Rates—Auctions and Models --- Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence --- Part III Insurance Risk and Asset Management --- Participating Life Insurance Contracts Under Risk Based Solvency Frameworks: How to Increase Capital Efficiency by Product Design --- Reducing Surrender Incentives Through Fee Structure in Variable Annuities --- A Variational Approach for Mean-Variance-Optimal Deterministic Consumption and Investment --- Risk Control in Asset Management: Motives and Concepts --- Worst-Case Scenario Portfolio Optimization Given the Probability of a Crash --- Improving Optimal Terminal Value Replicating Portfolios --- Part IV Computational Methods for Risk Management --- Risk and Computation --- Extreme Value Importance Sampling for Rare Event Risk Measurement --- A Note on the Numerical Evaluation of the Hartman–Watson Density and Distribution Function --- Computation of Copulas by Fourier Methods --- Part V Dependence Modelling --- Goodness-of-fit Tests for Archimedean Copulas in High Dimensions --- Duality in Risk Aggregation --- Some Consequences of the Markov Kernel Perspective of Copulas --- Copula Representations for Invariant Dependence Functions --- Nonparametric Copula Density Estimation Using a Petrov–Galerkin Projection

Beschreibung / Inhaltsverzeichnis: Wetlands and Water Framework Directive: protection, management and climate change --- Synergies and Conflicts between Water Framework Directive and Natura 2000: Legal requirements, technical guidance and experiences from practice --- Can Natura 2000 Sites Benefit from River Basin Management Planning Under a Changing Climate? Lessons from Germany --- Do water management and climate-adapted management of wetlands interfere in practice? Lessons from the Biebrza Valley, Poland --- Wetlands in river valleys as an effect of fluvial processes and anthropopression --- New vision of the role of land reclamation systems in nature protection and water management

Beschreibung / Inhaltsverzeichnis: Introduction: concept of TAIGA --- Geochemical constraints on potential biomass sustained by subseafloor water-rock interactions --- Microbial cell densities, community structures, and growth in the hydrothermal plumes of subduction hydrothermal systems --- Systematics of distributions of various elements between ferromanganese oxides and seawater from natural observation, thermodynamics, and structures --- Evaluating hydrothermal system evolution using geochronological dating and biological diversity analyses --- Quantification of microbial communities in hydrothermal vent habitats of the Southern Mariana Trough and the Mid-Okinawa Trough --- Development of hydrothermal and frictional experimental systems to simulate sub-seafloor water–rock–microbe interactions --- Experimental hydrogen production in hydrothermal and fault systems: Significance for habitability of subseafloor H2 chemoautotroph microbial ecosystems --- Experimental assessment of microbial effects on chemical interaction between seafloor massive sulfides and seawater at 4℃ --- A compilation of the stable isotopic compositions of carbon, nitrogen, and sulfur in soft body parts of animals collected from deep-sea hydrothermal vent and methane seep fields: variations in energy source and importance of subsurface microbial processes in the sediment-hosted systems --- Tectonic background of four hydrothermal fields along the Central Indian Ridge --- Indian Ocean hydrothermal systems: seafloor hydrothermal activities, physical and chemical characteristics of hydrothermal fluids, and vent-associated biological communities --- Petrology and geochemistry of mid-ocean ridge basalts from the southern Central Indian Ridge --- Petrology of peridotites and related gabbroic rocks around the Kairei-hydrothermal field in the Central Indian Ridge --- Distribution and Biogeochemical Properties of Hydrothermal Plumes in the Rodriguez Triple Junction --- Vent fauna in the Central Indian Ridge --- The mantle dynamics, the crustal formation, and the hydrothermal activity of the Southern Mariana Trough back-arc Basin --- Seismic structure and seismicity in the Southern Mariana Trough and their relation to hydrothermal activity --- Electrical resistivity structure of the Snail site at the Southern Mariana Trough spreading center --- Asymmetric seafloor spreading of the southern Mariana Trough back-arc basin --- Geochemical characteristics of active backarc basin volcanisms at the southern end of Mariana Trough --- Mineralogical and geochemical characteristics of hydrothermal minerals collected from hydrothermal vent fields in the Southern Mariana spreading center --- Dating of hydrothermal mineralization in active hydrothermal fields in the Southern Mariana Trough --- Intra-field variation of prokaryotic communities on and below the seafloor in the back-arc hydrothermal system of the Southern Mariana Trough --- Vent fauna in the Mariana Trough --- Population history of a hydrothermal vent-endemic snail Alviniconcha hessleri in the Mariana Trough --- Hydrothermal activity in the Okinawa Trough backarc basin -geological background and hydrothermal mineralization- --- Active rifting structures in Iheya Graben and adjacent area of the mid-Okinawa Trough observed through seismic reflection surveys --- ESR dating of barite in sea-floor hydrothermal sulfide deposits in the Okinawa Trough --- Fluid geochemistry of high-temperature hydrothermal fields in the Okinawa Trough --- Sediment‒pore water system associated with native sulfur formation at Jade hydrothermal field in Okinawa Trough --- Comparative investigation of microbial communities associated with hydrothermal activities in the Okinawa Trough --- In situ determination of bacterial growth in mixing zone of hydrothermal vent field on the Hatoma Knoll, Southern Okinawa Trough --- Vent Fauna in the Okinawa Trough --- Brief report of side-scan sonar observations around the Yokoniwa NTO massif --- Examination of volcanic activity: AUV and submersible observations of fine-scale lava flow distributions along the Southern Mariana Trough spreading axis --- Brief report of side-scan sonar imagery observations of the Archaean, Pika, and Urashima hydrothermal sites --- The Yoron Hole: the shallowest hydrothermal site in the Okinawa Trough --- The Irabu Knoll: Hydrothermal site at the eastern edge of the Yaeyama Graben --- Tarama Knoll: Geochemical and biological profiles of hydrothermal activity --- Petrography and geochemistry of basement rocks drilled from Snail, Yamanaka, Archean, and Pika hydrothermal fields at the Southern Mariana Trough by Benthic Multi-coring System (BMS) --- Pore fluid chemistry beneath active hydrothermal fields in the mid-Okinawa Trough: Results of shallow drilling by BMS during TAIGA11 cruise --- The characteristics of the seafloor massive sulfide deposits at the Hakurei Site in the Izena Hole, the Middle Okinawa Trough --- Occurrence of hydrothermal alteration minerals at the Jade hydrothermal field, in the Izena Hole, mid-Okinawa Trough --- Geochemistry of hydrothermal fluids collected from active hydrothermal systems in the southern Mariana Trough backarc spreading center --- Gamma ray doses in water around sea floor hydrothermal area in South Mariana --- 226Ra-210Pb and 228Ra-228Th dating of barite in submarine hydrothermal sulfide deposits collected at Okinawa Trough and South Mariana Trough --- OSL dating of sea floor sediments at the Okinawa Trough --- Immediate change of radiation doses from hydrothermal deposits --- Periodic behavior of deep sea current in the Hatoma Knoll hydrothermal system --- The gelatinous macroplankton community at the Hatoma Knoll hydrothermal vent

Beschreibung / Inhaltsverzeichnis: 1. Supershear Earthquake Ruptures --- Theory, Methods, Laboratory Experiments and Fault Superhighways: An Update.- 2. Civil Protection Achievements and Critical Issues in Seismology and Earthquake Engineering Research.- 3. Earthquake Risk Assessment: Certitudes, Fallacies, Uncertainties and the Quest for Soundness.- 4. Variability and Uncertainty in Empirical Ground-Motion Prediction for Probabilistic Hazard and Risk Analyses.- 5. Seismic Code Developments for Steel and Composite Structures.- 6. Seismic Analyses and Design of  Foundation Soil Structure Interaction.- 7. Performance-based Seismic Design and Assessment of Bridges.- 8. An Algorithm to Justify the Design of Single Story Precast Structures.- 9. Developments in Seismic Design of Tall Buildings: Preliminary Design of Coupled Core Wall Systems --- 10. Seismic Response of  Underground Lifeline Systems.- 11. Seismic Performance of Historical Masonry Structures Through Pushover and Nonlinear Dynamic Analyses.- 12. Developments in Ground Motion Predictive Models and Accelerometric Data Archiving in the Broader European Region --- 13. Towards the “Ultimate Earthquake-proof” Building: Development of an Integrated Low-damage System.- 14. Archive of Historical Earthquake Data for the European-Mediterranean Area --- 15. A Review and Some New Issues on the Theory of  the H/V Technique for Ambient Vibrations.- 16. Macroseismic Intervention Group: The Necessary Field Observation.- 17. Bridging the Gap Between Nonlinear Seismology as Reality and Earthquake Engineering --- 18. The Influence of Earthquake Magnitude on Hazard Related to Induced Seismicity.- 19. On the Origin of Mega-thrust Earthquakes.  

Beschreibung / Inhaltsverzeichnis: Part I Markets, Regulation, and Model Risk --- A Random Holding Period Approach for Liquidity-Inclusive Risk Management --- Regulatory Developments in Risk Management: Restoring Confidence in Internal Models --- Model Risk in Incomplete Markets with Jumps --- Part II Financial Engineering --- Bid-Ask Spread for Exotic Options Under Conic Finance --- Derivative Pricing Under the Possibility of Long Memory in the supOU Stochastic Volatility Model --- A Two-Sided BNS Model for Multicurrency FX Markets --- Modeling the Price of Natural Gas with Temperature and Oil Price as Exogenous Factors --- Copula-Specific Credit Portfolio Modeling --- Implied Recovery Rates—Auctions and Models --- Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence --- Part III Insurance Risk and Asset Management --- Participating Life Insurance Contracts Under Risk Based Solvency Frameworks: How to Increase Capital Efficiency by Product Design --- Reducing Surrender Incentives Through Fee Structure in Variable Annuities --- A Variational Approach for Mean-Variance-Optimal Deterministic Consumption and Investment --- Risk Control in Asset Management: Motives and Concepts --- Worst-Case Scenario Portfolio Optimization Given the Probability of a Crash --- Improving Optimal Terminal Value Replicating Portfolios --- Part IV Computational Methods for Risk Management --- Risk and Computation --- Extreme Value Importance Sampling for Rare Event Risk Measurement --- A Note on the Numerical Evaluation of the Hartman–Watson Density and Distribution Function --- Computation of Copulas by Fourier Methods --- Part V Dependence Modelling --- Goodness-of-fit Tests for Archimedean Copulas in High Dimensions --- Duality in Risk Aggregation --- Some Consequences of the Markov Kernel Perspective of Copulas --- Copula Representations for Invariant Dependence Functions --- Nonparametric Copula Density Estimation Using a Petrov–Galerkin Projection