Probability representations of solutions to the heat equation

DOI10.1007/BF02829609zbMath1052.35065arXivmath/0310262OpenAlexW2086387131MaRDI QIDQ1879454

B. Rajeev, Sundaram Thangavelu

Publication date: 22 September 2004

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310262

zbMATH Keywords

Brownian motiontranslation operatorsinfinite dimensional stochastic differential equations

Mathematics Subject Classification ID

Heat equation (35K05) Applications of stochastic analysis (to PDEs, etc.) (60H30) Initial value problems for second-order parabolic equations (35K15)

Related Items (10)

An Itō formula in the space of tempered distributions ⋮ Translation invariant diffusions in the space of tempered distributions ⋮ Stochastic PDEs in \(\mathcal{S}'\) for SDEs driven by Lévy noise ⋮ Lévy flows and associated stochastic PDEs ⋮ Probabilistic representations of solutions of the forward equations ⋮ Time-dependent tempered generalized functions and Itô’s formula ⋮ STOCHASTIC HEAT EQUATION ON ALGEBRA OF GENERALIZED FUNCTIONS ⋮ A class of stochastic differential equations with pathwise unique solutions ⋮ THE MONOTONICITY INEQUALITY FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS ⋮ Solutions of SPDE's associated with a stochastic flow

Cites Work

• Semimartingales: A course on stochastic processes
• Diffusion approximation of nuclear space-valued stochastic differential equations driven by Poisson random measures
• THE MONOTONICITY INEQUALITY FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
• Functional Integration and Partial Differential Equations. (AM-109)
• Diffusions and Elliptic Operators
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