Backward stochastic differential equations associated to a symmetric Markov process

被引：0

作者：

Bally V. ^{[1
]}

Pardoux E. ^{[2
]}

Stoica L. ^{[3
]}

机构：

[1] Université du Maine, Faculté des Sciences, Lab. de Statistique et Processus, 72085, Le Mans Cedex 9, Av. Olivier Messiaen

[2] LATP/CMI, Université de Provence, 13 453 Marseille Cedex 13, 39, rue F. Joliot Curie

[3] Université de Bucarest, Fac. de Mathématiques, Bucarest, ro70109

来源：

Potential Analysis | 2005年 / 22卷 / 1期

关键词：

Backward stochastic differential equations; Divergence form semilinear parabolic partial differential equations; Symmetric Markov processes;

D O I：

10.1007/s11118-004-6457-3

中图分类号：

学科分类号：

摘要：

We consider a second order semi-elliptic differential operator L with measurable coefficients, in divergence form, and the semilinear parabolic system of PDE's (∂t + L)u(t,x) + f(t,x,u,∇uσ) = 0, ∀0 ≤ t ≤ T, u(T,x) = Φ(x). We solve this system in the framework of Dirichlet spaces and employ the symmetric Markov process of infinitesimal operator L in order to obtain a precised version of the solution u by solving the corresponding system of backward stochastic differential equations. This precised version verifies pointwise the so called "mild equation", which is equivalent to the above PDE. As a technical ingrediend we prove a representation theorem for arbitrary martingales which generalises a result of Fukushima for martingale additive functionals. The nonlinear term f satisfies a monotonicity condition with respect to u and a Lipschitz condition with respect to ∇u. © Springer 2005.

引用

页码：17 / 60

页数：43

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