Construction of strong solutions of SDE's via Malliavin calculus

DOI10.1016/j.jfa.2009.11.010zbMath1195.60082OpenAlexW2017235256MaRDI QIDQ971842

Thilo Meyer-Brandis, Frank Norbert Proske

Publication date: 17 May 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.11.010

zbMATH Keywords

Malliavin calculusstochastic differential equationsstrong solutions of SDE

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic calculus of variations and the Malliavin calculus (60H07)

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Cites Work

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• Unnamed Item
• Explicit representation of strong solutions of SDEs driven by infinite-dimensional Lévy processes
• A characterization of Hida distributions
• Dirichlet forms and analysis on Wiener space
• White noise calculus and Fock space
• A class of stochastic differential equations with non-Lipschitzian coefficients: Pathwise uniqueness and no explosion
• Strong solutions of stochastic equations with singular time dependent drift
• Integration with respect to local time
• Diffusion approximation of nuclear space-valued stochastic differential equations driven by Poisson random measures
• Existence of strong solutions for Itô's stochastic equations via approximations
• Properties of perpetual integral functionals of Brownian motion with drift
• On the existence and explicit representability of strong solutions of Lévy noise driven SDE's with irregular coefficients
• On the uniqueness of solutions of stochastic differential equations
• ON ESTIMATES OF THE MAXIMUM OF A SOLUTION OF A PARABOLIC EQUATION AND ESTIMATES OF THE DISTRIBUTION OF A SEMIMARTINGALE
• On Stochastic Differential Equations with Locally Unbounded Drift
• On the Strong Solutions of Stochastic Differential Equations
• ON EXPLICIT STRONG SOLUTION OF ITÔ–SDE'S AND THE DONSKER DELTA FUNCTION OF A DIFFUSION
• Stochastic differential equations—some new ideas
• On a stochastic integral equation
• A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT

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