Transformation of the Wiener measure under non-invertible shifts

DOI10.1007/BF01206229zbMath0801.60031MaRDI QIDQ1333581

Ali Süleyman Üstünel, Moshe Zakai

Publication date: 21 November 1994

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

Girsanov-type densityperturbation of the identityRadon-Nikodym density for the image of the Wiener measure

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic calculus of variations and the Malliavin calculus (60H07) Continuity and singularity of induced measures (60G30)

Related Items (23)

Tangent processes on Wiener space ⋮ Estimation for the additive Gaussian channel and Monge-Kantorovitch measure transportation ⋮ Random rotations of the Wiener path ⋮ Girsanov theorem for anticipative shifts on Poisson space ⋮ The Sard inequality on Wiener space ⋮ Measures induced on Wiener space by monotone shifts ⋮ A second-order Stratonovich differential equation with boundary conditions ⋮ A note on the Malliavin-Sobolev spaces ⋮ Embedding the abstract Wiener space in a probability space ⋮ Flows associated to adapted vector fields on the Wiener space ⋮ A note on the CIR process and the existence of equivalent martingale measures ⋮ Laplace transform identities and measure-preserving transformations on the Lie-Wiener-Poisson spaces ⋮ Integration by parts on the law of the reflecting Brownian motion ⋮ Convexity inequalities and optimal transport of infinite-dimensional measures ⋮ Some covariance inequalities in Wiener space ⋮ On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions ⋮ Invertibility of adapted perturbations of the identity on abstract Wiener space ⋮ On the uniform integrability of the Radon-Nikodym densities for Wiener measure ⋮ Differentiable measures and the Malliavin calculus ⋮ Entropy, invertibility and variational calculus of adapted shifts on Wiener space ⋮ The notion of convexity and concavity on Wiener space ⋮ The Clark-Ocone formula for vector valued Wiener functionals ⋮ \(H\)-\(C^1\) maps and elliptic SPDEs with polynomial and exponential perturbations of Nelson's Euclidean free field

Cites Work

• Anticipative Girsanov transformations
• Generalized stochastic integrals and the Malliavin calculus
• Degree theory for Wiener maps
• Dirichlet forms and analysis on Wiener space
• Transformation of Wiener measure under anticipative flows
• Applications of the degree theorem to absolute continuity on Wiener space
• On nonlinear transformations of Gaussian measures
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Transformation of the Wiener measure under non-invertible shifts