Nonlinear transformations of the canonical Gauss measure on Hilbert space and absolute continuity

DOI10.1007/BF00994912zbMath0803.60050OpenAlexW2056501228MaRDI QIDQ1332519

Rajeeva L. Karandikar, Gopinath Kallianpur

Publication date: 3 January 1995

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00994912

zbMATH Keywords

uniform integrabilityabstract Wiener spaceliftingsabsolute continuitycylindrical measureGokhberg-Krejn factorizationcanonical Gauss measureCarleman-Fredholm determinantsKusuoka's formulanonlinear transformation of Wiener measureRamer-Itô integralweak Gateaux- differentiability

Mathematics Subject Classification ID

Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11)

Related Items (2)

Gaussian measures on linear spaces ⋮ Randomness and nonlinear evolution equations

Cites Work

• Anticipative Girsanov transformations
• Equivalence and perpendicularity of Gaussian processes
• Non-anticipative representations of equivalent Gaussian processes
• On the structure of independence on Wiener space
• On nonlinear transformations of Gaussian measures
• Integration and Nonlinear Transformations In Hilbert Space
• Homogeneous Chaos, p-Forms, Scaling and the Feynman Integral
• An RKHS approach to detection and estimation problems-- III: Generalized innovations representations and a likelihood-ratio formula
• The Transformation of Wiener Integrals by Nonlinear Transformations
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