Malliavin calculus in abstract Wiener space using infinitesimals

DOI10.1016/S0001-8708(02)00033-6zbMath1018.60058OpenAlexW2048518870MaRDI QIDQ1874460

Horst Osswald

Publication date: 25 May 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0001-8708(02)00033-6

zbMATH Keywords

Malliavin calculusnonstandard analysisabstract Wiener spaces

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Nonstandard models in mathematics (03H05)

Related Items (10)

On the Clark Ocone formula for the abstract Wiener space ⋮ Uncorrelatedness and orthogonality for vector-valued processes ⋮ Computation of the kernels of Lévy functionals and applications ⋮ Independent random partial matching with general types ⋮ A nonstandard Lévy-Khintchine formula and Lévy processes ⋮ On the continuity of pathwise solutions to Langevin equations in infinite dimensions ⋮ Malliavin calculus for product measures on ℝ^ℕ based on chaos ⋮ A smooth approach to Malliavin calculus for Lévy processes ⋮ On anticipative Girsanov transformations for Lévy processes ⋮ From Probability Measures to Each Lévy Triplet and Back

Cites Work

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• Characterization of the law of the iterated logarithm in Banach spaces
• Dirichlet forms and analysis on Wiener space
• Gaussian measures in Banach spaces
• Nonstandard integration theory in topological vector lattices
• On the Clark Ocone formula for the abstract Wiener space
• Embedding the abstract Wiener space in a probability space
• An infinitesimal approach to stochastic analysis
• Infinitesimals in Action
• Measurable Functions on Hilbert Space

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