论文信息 - Stochastic variational formula for fundamental solutions of parabolic PDE

Stochastic variational formula for fundamental solutions of parabolic PDE

Letp(t, x, y) be the fundamental solution of a linear, second order partial differential equation of parabolic type. The functionI = −logp satisfies a nonlinear parabolic equation, which is the dynamic programming equation associated with a control problem of stochastic calculus of variations type. This gives a stochastic variational formula forp. The proof depends on a result of Molchanov about the asymptotic behavior ofp(t, x, y) for smallt.

Wendell H. Fleming | W. Fleming | S. Sheu | Sheunn-Jyi Sheu

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