Time-reversal and elliptic boundary value problems

DOI10.1214/08-AOP427zbMath1187.60064arXiv0907.4301MaRDI QIDQ2270608

Tu-Sheng Zhang, Zhen-Qing Chen

Publication date: 28 July 2009

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.4301

zbMATH Keywords

diffusionweak solutionquadratic formpartial differential equationboundary value problemDirichlet formtime-reversalmeasurable coefficientsprobabilistic representationdivergence form operatorFeynman-Kac transformGirsanov transformh-transformmultiplicative functional

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Boundary value problems for second-order elliptic equations (35J25) Dirichlet forms (31C25) PDEs with low regular coefficients and/or low regular data (35R05) Stochastic integrals (60H05) Martingales and classical analysis (60G46) Local time and additive functionals (60J55) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Multiplicative functionals and Markov processes (60J57)

Related Items (14)

Neumann boundary value problems for elliptic operators with measure-valued coefficients ⋮ A probabilistic approach to Neumann problems for elliptic PDEs with nonlinear divergence terms ⋮ Backward stochastic differential equations and Dirichlet problems of semilinear elliptic operators with singular coefficients ⋮ Probabilistic representations of solutions of elliptic boundary value problem and non-symmetric semigroups ⋮ Mixed boundary value problems of semilinear elliptic PDEs and BSDEs with singular coefficients ⋮ Estimates of heat kernels with Neumann boundary conditions ⋮ \(L^p\)-independence of spectral bounds of generalized non-local Feynman-Kac semigroups ⋮ The probabilistic solution of a system of semilinear elliptic PDEs under the third boundary conditions ⋮ Dirichlet boundary value problems for elliptic operators with measure data ⋮ A probabilistic approach to mixed boundary value problems for elliptic operators with singular coefficients ⋮ A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients ⋮ Stochastic calculus over symmetric Markov processes with time reversal ⋮ BACKWARD SDEs AND SOBOLEV SOLUTIONS FOR SEMILINEAR PARABOLIC PDEs WITH SINGULAR COEFFICIENTS ⋮ Neumann boundary problems for parabolic partial differential equations with divergence terms

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