Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. (English) Zbl 0739.60060

Peng, Shige

Stochastics Stochastics Rep. 37, No. 1-2, 61-74 (1991).

Summary: A probabilistic interpretation for systems of second order quasilinear parabolic partial differential equations is obtained by introducing a kind of backward stochastic differential equation. Similar applications to systems of elliptic partial differential equations and to optimal control problems are also briefly discussed.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
93E20	Optimal stochastic control
60J60	Diffusion processes

Keywords:

Feynman-Kac formula; parabolic partial differential equations; optimal control problems