Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients

DOI10.1007/s10959-011-0350-yzbMath1255.60103arXiv0902.1148OpenAlexW2102135598MaRDI QIDQ430972

Huaizhong Zhao, Qi Zhang

Publication date: 26 June 2012

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.1148

zbMATH Keywords

weak convergencecompact embeddingbackward stochastic differential equationsprobabilistic representation of weak solution

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Initial value problems for second-order parabolic equations (35K15) Weak solutions to PDEs (35D30) Solutions to PDEs in closed form (35C05)

Related Items

Dynamic programming principle and associated Hamilton-Jacobi-Bellman equation for stochastic recursive control problem with non-Lipschitz aggregator ⋮ Quasi-linear PDEs and forward-backward stochastic differential equations: weak solutions ⋮ Sobolev space weak solutions to one kind of quasilinear parabolic partial differential equations related to forward-backward stochastic differential equations ⋮ SPDEs with polynomial growth coefficients and the Malliavin calculus method ⋮ BSDEs with polynomial growth generators in a defaultable market ⋮ A study of backward stochastic differential equation on a Riemannian manifold ⋮ Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations ⋮ Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs ⋮ Backward doubly stochastic differential equations with polynomial growth coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adapted solution of a backward stochastic differential equation
• Short time behavior of the heat kernel and its logarithmic deviatives
• Sobolev solution for semilinear PDE with obstacle under monotonicity condition
• Infinite-dimensional dynamical systems in mechanics and physics
• Stochastic flows acting on Schwartz distributions
• Backward stochastic differential equations with continuous coefficient
• Backward stochastic differential equations and partial differential equations with quadratic growth.
• Constructing gamma-martingales with prescribed limit, using backwards SDE
• Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients
• BSDE with quadratic growth and unbounded terminal value
• Stationary solutions of SPDEs and infinite horizon BDSDEs
• A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.'s
• Functional Integration and Partial Differential Equations. (AM-109)
• ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS
• Asymptotic evaluation of certain markov process expectations for large time, I
• Approximate travelling waves for generalized KPP equations and classical mechanics
• Backward Stochastic Differential Equations in Finance
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• On Distributions of Certain Wiener Functionals
• Weak solutions for SPDE's and backward doubly stochastic differential equations

This page was built for publication: Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients