Stochastic calculus of variations for stochastic partial differential equations

DOI10.1016/0022-1236(88)90015-8zbMath0653.60046OpenAlexW1981477920MaRDI QIDQ1107903

Daniel L. Ocone

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0022-1236(88)90015-8

zbMATH Keywords

Malliavin calculusGalerkin approximationsHörmander's hypoellipticity theoremcoercivity conditionZakai equation of nonlinear filtering

Mathematics Subject Classification ID

Signal detection and filtering (aspects of stochastic processes) (60G35) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

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Cites Work

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• Absolue continuité de probabilités de transition par rapport à une mesure gaussienne dans un espace de Hilbert. (Absolute continuity of transition probabilities with respect to a Gaussian measure in a Hilbert space)
• Lectures on stochastic differential equations and Malliavin calculus
• The Malliavin calculus
• Generalized stochastic integrals and the Malliavin calculus
• Probability densities for conditional statistics in the cubic sensor problem
• The Malliavin calculus, a functional analytic approach
• Diffusions conditionnelles. II. Générateur conditionel. Application au filtrage
• Derivatives of Wiener functionals and absolute continuity of induced measures
• Régularité des lois conditionnelles en théorie du filtrage non-linéaire et calcul des variations stochastique
• Sur l'unicité retrograde des équations paraboliques et quelques questions voisines
• Algebraic and Geometric Methods in Nonlinear Filtering
• The partial malliavin calculus and its application to non-linear filtering
• Stochastic partial differential equations and filtering of diffusion processes
• [https://portal.mardi4nfdi.de/wiki/Publication:3889862 Martingales, the Malliavin calculus and hypoellipticity under general H�rmander's conditions]
• Moments of Semilinear Random Evolutions
• Controllability for Distributed Bilinear Systems
• ON CONDITIONAL DISTRIBUTIONS OF DIFFUSION PROCESSES
• An introduction to the theory of large deviations