• Corpus ID: 115171094

Analysis on Wiener Space and Applications

  title={Analysis on Wiener Space and Applications},
  author={Ali Suleyman Ustunel},
The aim of this book is to give a rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of the Stochastic Calculus of Variations of Paul Malliavin. 
Measure Invariance on the Lie-Wiener Path Space
In this chapter we extend some recent results on moment identities, Hermite polynomials, and measure invariance properties on the Wiener space, to the setting of path spaces over Lie groups. In
Math 7770 : Analysis and Probability on Infinite-Dimensional Spaces
• Rn has a natural measure space structure; namely, Lebesgue measure m on the Borel σalgebra. The most important property of Lebesgue measure is that it is invariant under translation. This leads to
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The invariance principle for M/M/1 and M/M/$\infty$ queues states that when properly renormalized (i.e. rescaled and centered), the Markov processes which describe these systems both converge to a
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On the Conditional Characteristic Functions of Second Order Wiener Functionals
We calculate the conditional characteristic functions of the elements of the second Wiener chaos using Ramer’s change of variables formula. This result is closely related to the Van-Vleck-Pauli
Transformation of the Wiener measure under non-invertible shifts
SummaryIn this paper we consider the transformation of measure induced by a not-necessarily-invertible perturbation of the identity. The Radon-Nikodym density for the image of the Wiener measure and
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Abstract We give sufficient conditions for the uniform integrability of the Radon–Nikodym derivatives of the images of Wiener measure under the non-linear transformations of the Wiener space. These
On an Independence Criterion for Multiple Wiener Integrals
Ustunel and Zakai have recently obtained a necessary and sufficient condition for two multiple Wiener integrals with respect to the same Brownian motion to be independent. In the present note, the
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SummaryLet (Ω,H, P) be an abstract Wiener space and define a shift on Ω byT(ω)=ω+F(ω) whereF is anH-valued random variable. We study the absolute continuity of the measuresPºT−1and (ΛFP)ºT∔1 with
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We prove the exponential integrability of Lipschitz functions in abstract Wiener spaces by using logarithmic Sobolev inequalities. We introduce two notions of Lipschitz continuity and apply the