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  • 1
    Monographie ausleihbar
    Monographie ausleihbar
    Stochastic Climate Models : [Chorin Workshop on Stochastic Climate Models] (2001)
    Boston, Mass. [u.a.] : Birkhäuser
    Dazugehörige Bände
    Details Verfügbarkeit
    Signatur: AWI A13-01-0091 ; PIK M 311-01-0414
    In: Progress in probability
    Materialart: Monographie ausleihbar
    Seiten: XXVI, 398 S.
    ISBN: 376436520X
    Serie: Progress in probability 49
    Zweigbibliothek: AWI Bibliothek
    Zweigbibliothek: PIK Bibliothek
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  • 2
    Digitale Medien
    Digitale Medien
    Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
    Details
    ISSN: 1467-9965
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: We consider simple models of financial markets with regular traders and insiders possessing some extra information hidden in a random variable that is accessible to the regular trader only at the end of the trading interval. The problems we focus on are the calculation of the additional utility of the insider and a study of his free lunch possibilities. The information drift—that is, the drift to eliminate in order to preserve the martingale property in the insider's filtration—turns out to be the crucial quantity needed to answer these questions. It is most elegantly described by the logarithmic Malliavin trace of the conditional laws of the insider information with respect to the filtration of the regular trader. Several examples are given to illustrate additional utility and free lunch possibilities. In particular, if the insider has advance knowledge of the maximal stock price process, given by a regular diffusion, arbitrage opportunities exist.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1111/1467-9965.00011
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  • 3
    Digitale Medien
    Digitale Medien
    Ito's formula for continuous (N,d)-processes (1984)
    Springer
    Probability theory and related fields 65 (1984), S. 535-562 
    Details
    ISSN: 1432-2064
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00531838
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  • 4
    Digitale Medien
    Digitale Medien
    Occupation densities for stochastic integral processes in the second Wiener chaos (1992)
    Springer
    Probability theory and related fields 91 (1992), S. 1-24 
    Details
    ISSN: 1432-2064
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The two-point distributions of Skorohod integral processes in the second Wiener chaos are mainly described by a Hilbert-Schmidt operatorT giving the mutual interaction of infinitely many Gaussian components and by simple multiplication operators. So are the Fourier transforms of their occupation measures. This enables us to use the well known Fourier analytic criterion discovered and elaborated by Berman to derive integral conditions for the existence of their occupation densities in terms of associated Hilbert-Schmidt operators. IfT is a trace class operator, we get a necessary and sufficient criterion, if it is not, still a sufficient one. In a case in which the interaction is particularly simple, we verify the appropriate integral condition and show that the results are essentially beyond the reach of “enlargement of filtrations” techniques of semimartingale theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01194487
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  • 5
    Digitale Medien
    Digitale Medien
    The asymptotic behaviour of local times and occupation integrals of theN-parameter Wiener process in R d (1994)
    Springer
    Probability theory and related fields 98 (1994), S. 47-75 
    Details
    ISSN: 1432-2064
    Schlagwort(e): 60G60 ; 60J55 ; 60G15 ; 60H05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary LetL(x, T),x∈R d ,T∈R + N , be the local time of theN-parameter Wiener processW taking values inR d . Even in the distribution valued casedd≧2N,L can be described in a series representation by means of multiple Wiener-Ito integrals. This setting proves to be a good starting point for the investigation of the asymptotic behaviour ofL(x, T) as |x|→0 and/orT∞ and of related occupation integrals $$X_T (f) = \int\limits_{[0,T]} f (W_S )$$ asT→∞. We obtain the rates of explosion in laws of the first order, i.e. normalized convergence laws forL(x, T) resp.X T (f), and of the second order, i.e. normalized convergence laws forL(x, T)−E(L(x, T)) resp.X T (f)−E(X T (f)).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01311348
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  • 6
    Digitale Medien
    Digitale Medien
    Normal forms for stochastic differential equations (1998)
    Springer
    Probability theory and related fields 110 (1998), S. 559-588 
    Details
    ISSN: 1432-2064
    Schlagwort(e): Mathematics Subject Classification: (1991) primary 60H10 ; 34F05; secondary 58F11 ; 93E03
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. We address the following problem from the intersection of dynamical systems and stochastic analysis: Two SDE dx t = ∑ j =0 m f j (x t )∘dW t j and dx t =∑ j =0 m g j (x t )∘dW t j in ℝ d with smooth coefficients satisfying f j (0)=g j (0)=0 are said to be smoothly equivalent if there is a smooth random diffeomorphism (coordinate transformation) h(ω) with h(ω,0)=0 and Dh(ω,0)=id which conjugates the corresponding local flows, where θ t ω(s)=ω(t+s)−ω(t) is the (ergodic) shift on the canonical Wiener space. The normal form problem for SDE consists in finding the “simplest possible” member in the equivalence class of a given SDE, in particular in giving conditions under which it can be linearized (g j (x)=Df j (0)x). We develop a mathematically rigorous normal form theory for SDE which justifies the engineering and physics literature on that problem. It is based on the multiplicative ergodic theorem and uses a uniform (with respect to a spatial parameter) Stratonovich calculus which allows the handling of non-adapted initial values and coefficients in the stochastic version of the cohomological equation. Our main result (Theorem 3.2) is that an SDE is (formally) equivalent to its linearization if the latter is nonresonant. As a by-product, we prove a general theorem on the existence of a stationary solution of an anticipative affine SDE. The study of the Duffing-van der Pol oscillator with small noise concludes the paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s004400050159
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  • 7
    Digitale Medien
    Digitale Medien
    Enlargement of the Wiener filtration by an absolutely continuous random variable via Malliavin’s calculus (1996)
    Springer
    Probability theory and related fields 106 (1996), S. 105-135 
    Details
    ISSN: 1432-2064
    Schlagwort(e): Mathematics Subject classification (1991): 60G48 ; 60H07 ; 60J65 ; 60H30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces of the (linearized) system. We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin’s calculus, we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s004400050059
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  • 8
    Digitale Medien
    Digitale Medien
    A note on the localization of two-parameter processes (1986)
    Springer
    Probability theory and related fields 73 (1986), S. 119-125 
    Details
    ISSN: 1432-2064
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Continuous two-parameter strong martingalesM andN with respect to a filtration, which is closely related to the filtration of a Wiener sheet, are constructed such thatM and the continuous increasing process [N] ofN (identical with the quadratic variation) cannot be “boundedly localized”: each stopping domainD for which the processesM or [N] stopped byD, are bounded must be contained in a nontrivial subset of ℝ + 2 which only depends onM orN.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01845995
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  • 9
    Digitale Medien
    Digitale Medien
    Regularity of Skorohod integral processes based on integrands in a finite Wiener chaos (1994)
    Springer
    Probability theory and related fields 98 (1994), S. 137-142 
    Details
    ISSN: 1432-2064
    Schlagwort(e): 60H05 ; 60G17 ; 60J65 ; 60G15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Letf be a square integrable kernel on them-dimensional unit cube,U the Skorohod integral process in them th Wiener chaos associated with it. Isoperimetric inequalities for functions on Wiener space yield the exponential integrability of the increments ofU. To this result we apply the majorizing measure technique to show thatU possesses a continuous version and give an upper bound of its modulus of continuity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01192510
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  • 10
    Digitale Medien
    Digitale Medien
    The transformation theorem for two-parameter pure jump martingales (1991)
    Springer
    Probability theory and related fields 89 (1991), S. 261-283 
    Details
    ISSN: 1432-2064
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary LetM be a martingale of pure jump type, i.e. the compensation of the process describing the total of the point jumps ofM in the plane.M can be uniformly approximated by martingales of bounded variation jumping only on finitely many axial parallel lines. Using this fact we prove a change of variables formula in which forC 4-functions f the processf(M) is described by integrals off (k) (M),k=1, 2, with respect to stochastic integrators of the types expected: a martingale, two processes behaving as martingales in one direction and as processes of bounded variation in the other, and one process of bounded variation. Hereby we are led to investigate two types of random measures not considered so far in this context. By combination with the integrators already known, they might complete the set needed for a general transformation formula.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01198787
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