Stochastic differential equations on the plane: Smoothness of the solution

DOI10.1016/0047-259X(89)90046-8zbMath0692.60044MaRDI QIDQ583719

Marta Sanz-Solé, David Nualart

Publication date: 1989

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

zbMATH Keywords

Malliavin calculusBrownian sheethypoellipticitynon-degeneracy conditionsHoermander's condition

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)

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Quasi-sure analysis of two-parameter stochastic differential equations, Random nonlinear wave equations: Smoothness of the solutions, The law of the solution to a nonlinear hyperbolic SPDE, Hyperbolic stochastic differential equations: Absolute continuity of the law of the solution at a fixed point, Fourier expansions with polynomial terms for random processes, Unnamed Item, Absolute continuity of the law of the solution to the 3-dimensional stochastic wave equation., Two-parameter diffusions random fields, Quasi-sure product variation of two-parameter smooth martingales on the Wiener space, Logarithmic estimates for the density of hypoelliptic two-parameter diffusions

Cites Work

• Lectures on stochastic differential equations and Malliavin calculus
• Existence of strong solutions for stochastic differential equations in the plane
• The Malliavin calculus, a functional analytic approach
• Derivatives of Wiener functionals and absolute continuity of induced measures
• Stochastic equations of hyperbolic type and a two-parameter Stratonovich calculus
• Stochastic integrals in the plane
• Malliavin calculus for two-parameter Wiener functionals
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