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

[1] W. Fleming. Logarithmic Transformations and Stochastic Control , 1982 .

[2] W. Fleming. Stochastic calculus of variations and mechanics , 1983 .

[3] K. Yasue. Quantum mechanics and stochastic control theory , 1981 .

[4] W. Fleming. Exit probabilities and optimal stochastic control , 1977 .

[5] Stanislav Molchanov,et al. DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY , 1975 .

[6] Edward Nelson. Dynamical Theories of Brownian Motion , 1967 .

[7] Optimal control and pathwise nonlinear filtering of nondegenerate diffusions , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[8] L. Papiez. Stochastic formulation of Feynman path integrals from the least action point of view , 1984 .

[9] S. Mitter,et al. Optimal control and nonlinear filtering for nondegenerate diffusion processes , 1982 .

[10] H. Kushner. On the Existence of Optimal Stochastic Controls , 1965 .

[11] Francesco Guerra,et al. Quantization of Dynamical Systems and Stochastic Control Theory , 1983 .

[12] B. Heimann,et al. Fleming, W. H./Rishel, R. W., Deterministic and Stochastic Optimal Control. New York‐Heidelberg‐Berlin. Springer‐Verlag. 1975. XIII, 222 S, DM 60,60 , 1979 .

[13] W. Fleming. The Cauchy problem for a nonlinear first order partial differential equation , 1969 .

[14] W. Fleming,et al. Deterministic and Stochastic Optimal Control , 1975 .