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