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Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space
We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space ( H , B , v ). An infinite dimensional conditioning...
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Wiener-Prozess, Satz von Donsker und Brown’sche Brücke
In diesem Kapitel werden zunächst das Wiener-Maß auf der sigma-Algebra der Borelmengen von C[0,1] und damit einhergehend der Wiener-Prozess...
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ASYMPTOTIC BEHAVIOR OF THE SOLUTION TO THE WIENER–HOPF EQUATION IN MEASURES
We consider a new equation of Wiener–Hopf type, where the kernel of the equation is a probability distribution, the inhomogeneous term is a measure...
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Relatively compact sets of Banach space-valued bounded-variation spaces
In this paper, we give criteria for the relatively compact sets of Banach space-valued bounded-variation spaces in the sense of Jordan and Banach...
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On the Wiener chaos expansion of the signature of a Gaussian process
We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with...
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Convolution Integral Operators in Variable Bounded Variation Spaces
Working in the frame of variable bounded variation spaces in the sense of Wiener, introduced by Castillo, Merentes, and Rafeiro, we prove convergence...
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Monte Carlo construction of cubature on Wiener space
In this paper, we investigate application of mathematical optimization to construction of a cubature formula on Wiener space, which is a weak...
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Further Properties and Examples of Abstract Wiener Spaces
This chapter is a continuation of the preceding one. Here we will derive a few more general properies of abstract Wiener spaces and then contstruct...
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Relation between Fourier series and Wiener algebras
New relations between the Banach algebras of absolutely convergent Fourier integrals of complex-valued measures of Wiener and various issues of...
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Multiplication operators between different Wiener-type variation spaces
In this article, we characterize all of the multipliers u which define continuous, invertible, finite and closed range, compact, and Fredholm...
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Optimal Couplings on Wiener Space and An Extension of Talagrand’s Transport Inequality
For a probability measure Q on Wiener space, Talagrand’s transport inequality takes the formWϰ (Q,P)2 ≤2H(Q|P), where theWasserstein distanceWϰ is...
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Subcritical Gaussian multiplicative chaos in the Wiener space: construction, moments and volume decay
We construct and study properties of an infinite dimensional analog of Kahane’s theory of Gaussian multiplicative chaos (Kahane in Ann Sci Math...
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Wiener-Prozess, Satz von Donsker und Brown’sche Brücke
In diesem Kapitel werden zunächst das Wiener-Maß auf der sigma-Algebra der Borelmengen von C[0,1] und damit einhergehend der Wiener-Prozess...
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Hermite Polynomials and Wiener Chaos Expansion
The essential result of this chapter states that the space of square integrable random variables generated by a continuous Gaussian martingale, can...
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Doob Decomposition, Dirichlet Processes, and Entropies on Wiener Space
As an extension of the Doob-Meyer decomposition of a semimartingale and the Fukushima representation of a Dirichlet process, we introduce a general...
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Asymptotic expansions in the central limit theorem for a branching Wiener process
We consider a branching Wiener process in ℝ d , in which particles reproduce as a super-critical Galton-Watson process and disperse according to a...
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Testing Cubature Formulae on Wiener Space Versus Explicit Pricing Formulae
Cubature is an effective way to calculate integrals in a finite dimensional space. Extending the idea of cubature to the infinite-dimensional Wiener...
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Elements of Wiener Analysis
We introduce some basic elements of Malliavin calculus also called stochastic calculus of variations by P. Malliavin himself. The fundamental...
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Total Variation Error Bounds for the Approximation of the Invariant Distribution of Parabolic Semilinear SPDEs Using the Standard Euler Scheme
We study the long time behavior of the standard linear implicit Euler scheme for the discretization of a class of erdogic parabolic semilinear SPDEs...