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  • Articles  (54)
  • Hindawi  (54)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Institute of Electrical and Electronics Engineers
  • Molecular Diversity Preservation International
  • Springer Nature
  • 2020-2022
  • 2010-2014  (54)
  • 1985-1989
  • 1960-1964
  • 2014  (42)
  • 2010  (12)
  • International Journal of Stochastic Analysis  (25)
  • 46742
  • Mathematics  (54)
  • Economics
  • Architecture, Civil Engineering, Surveying
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  • Articles  (54)
Source
Publisher
  • Hindawi  (54)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Institute of Electrical and Electronics Engineers
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Years
  • 2020-2022
  • 2010-2014  (54)
  • 1985-1989
  • 1960-1964
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  • Mathematics  (54)
  • Economics
  • Architecture, Civil Engineering, Surveying
  • 1
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    From Pseudorandom Walk to Pseudo-Brownian Motion: First Exit Time from a One-Sided or a Two-Sided Interval (2014)
    Hindawi
    Details
    Publication Date: 2014-03-27
    Description: Let be a positive integer, a positive constant and be a sequence of independent identically distributed pseudorandom variables. We assume that the ’s take their values in the discrete set and that their common pseudodistribution is characterized by the (positive or negative) real numbers for any . Let us finally introduce the associated pseudorandom walk defined on by and for . In this paper, we exhibit some properties of . In particular, we explicitly determine the pseudodistribution of the first overshooting time of a given threshold for as well as that of the first exit time from a bounded interval. Next, with an appropriate normalization, we pass from the pseudorandom walk to the pseudo-Brownian motion driven by the high-order heat-type equation . We retrieve the corresponding pseudodistribution of the first overshooting time of a threshold for the pseudo-Brownian motion (Lachal, 2007). In the same way, we get the pseudodistribution of the first exit time from a bounded interval for the pseudo-Brownian motion which is a new result for this pseudoprocess.
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    Topics: Mathematics
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  • 2
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    with Setup Time, Bernoulli Vacation, Break Down, and Delayed Repair (2014)
    Hindawi
    Details
    Publication Date: 2014-04-01
    Description: We present a single server in which customers arrive in batches and the server provides service one by one. The server provides two heterogeneous service stages such that service time of both stages is different and mandatory to all arriving customers in such a way that, after the completion of first stage, the second stage should also be provided to the customers. The server may subject to random breakdowns with brake down rate and, after break down, it should be repaired but it has to wait for being repaired and such waiting time is called delay time. Both the delay time and repair time follow exponential distribution. Upon the completion of the second stage service, the server will go for vacation with probability or stay back in the system probability , if any. The vacation time follows general (arbitrary) distribution. Before providing service to a new customer or a batch of customers that joins the system in the renewed busy period, the server enters into a random setup time process such that setup time follows exponential distribution. We discuss the transient behavior and the corresponding steady state results with the performance measures of the model.
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    Topics: Mathematics
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  • 3
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    A Discrete-Time Queue with Balking, Reneging, and Working Vacations (2014)
    Hindawi
    Details
    Publication Date: 2014-10-30
    Description: This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.
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    Topics: Mathematics
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  • 4
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    Limit Properties of Transition Functions of Continuous-Time Markov Branching Processes (2014)
    Hindawi
    Details
    Publication Date: 2014-10-20
    Description: Consider the Markov Branching Process with continuous time. Our focus is on the limit properties of transition functions of this process. Using differential analogue of the Basic Lemma we prove local limit theorems for all cases and observe invariant properties of considering process.
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    Topics: Mathematics
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  • 5
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    Optimal Foreign Exchange Rate Intervention in Lévy Markets (2014)
    Hindawi
    Details
    Publication Date: 2014-11-27
    Description: This paper considers an exchange rate problem in Lévy markets, where the Central Bank has to intervene. We assume that, in the absence of control, the exchange rate evolves according to Brownian motion with a jump component. The Central Bank is allowed to intervene in order to keep the exchange rate as close as possible to a prespecified target value. The interventions by the Central Bank are associated with costs. We present the situation as an impulse control problem, where the objective of the bank is to minimize the intervention costs. In particular, the paper extends the model by Huang, 2009, to incorporate a jump component. We formulate and prove an optimal verification theorem for the impulse control. We then propose an impulse control and construct a value function and then verify that they solve the quasivariational inequalities. Our results suggest that if the expected number of jumps is high the Central Bank will intervene more frequently and with large intervention amounts hence the intervention costs will be high.
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    Topics: Mathematics
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  • 6
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    Backward Stochastic Differential Equations Approach to Hedging, Option Pricing, and Insurance Problems (2014)
    Hindawi
    Details
    Publication Date: 2014-09-12
    Description: In the present work we give a self-contained introduction to financial mathematical models characterized by noise of Lévy type in the framework of the backward stochastic differential equations theory. Such techniques will be then used to analyse an innovative model related to insurance and death processes setting.
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  • 7
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    Strong Law of Large Numbers for Hidden Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degrees (2014)
    Hindawi
    Details
    Publication Date: 2014-12-11
    Description: We study strong limit theorems for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees. We mainly establish the strong law of large numbers for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees and give the strong limit law of the conditional sample entropy rate.
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  • 8
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    A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet (2014)
    Hindawi
    Details
    Publication Date: 2014-05-26
    Description: We consider the problem of switching a large number of production lines between two modes, high production and low production. The switching is based on the optimal expected profit and cost yields of the respective production lines and considers both sides of the balance sheet. Furthermore, the production lines are all assumed to be interconnected through a coupling term, which is the average of all optimal expected yields. Intuitively, this means that each individual production line is compared to the average of all its peers which acts as a benchmark. Due to the complexity of the problem, we consider the aggregated optimal expected yields, where the coupling term is approximated with the mean of the optimal expected yields. This turns the problem into a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.
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    Topics: Mathematics
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  • 9
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    Efficient Variable Step Size Approximations for Strong Solutions of Stochastic Differential Equations with Additive Noise and Time Singularity (2014)
    Hindawi
    Details
    Publication Date: 2014-07-03
    Description: We consider stochastic differential equations with additive noise and conditions on the coefficients in those equations that allow a time singularity in the drift coefficient. Given a maximum step size, , we specify variable (adaptive) step sizes relative to which decrease as the time node points approach the singularity. We use an Euler-type numerical scheme to produce an approximate solution and estimate the error in the approximation. When the solution is restricted to a fixed closed time interval excluding the singularity, we obtain a global pointwise error of order . An order of error for any is obtained when the approximation is run up to a time within of the singularity for an appropriate choice of exponent . We apply this scheme to Brownian bridge, which is defined as the nonanticipating solution of a stochastic differential equation of the type under consideration. In this special case, we show that the global pointwise error is of order , independent of how close to the singularity the approximation is considered.
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  • 10
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    Influence of Gestation Delay and Predator’s Interference in Predator-Prey Interaction under Stochastic Environment (2014)
    Hindawi
    Details
    Publication Date: 2014-04-09
    Description: Previous experimental and theoretical studies suggest that predator’s interference in predator-prey relationship provides better descriptions of predator’s feeding over a range of predator-prey abundances. Also biological delays and environmental stochasticity play an important role to describe the system and its values. In this present study, I consider a Gaussian white-noise induced stochastic predator-prey model with the Beddington-DeAngelis functional response and gestation delay. Stochastic stability is measured by second order moment terms by calculating the nonequilibrium fluctuation of the nondelayed system and Fourier transform technique depicts the fluctuation of stochastic stability by introducing time lag. Different dynamical behaviors for both situations have been illustrated numerically also. The biological implications of my analytical and numerical findings are discussed critically.
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    Topics: Mathematics
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