论文信息 - A topology for Markov controls

A topology for Markov controls

For a controlled nondegenerate diffusion, a topology is defined on the set of all Markov relaxed controls, which is compact metrizable and with respect to which the resultant law of the diffusion with prescribed initial law is a continuous function of the control.

V. Borkar

[1] P. Meyer. Probability and potentials , 1966 .

[2] D. Aronson,et al. Bounds for the fundamental solution of a parabolic equation , 1967 .

[3] P. Varaiya,et al. On the Solutions of a Stochastic Control System. II , 1971 .

[4] V. Benes. Existence of Optimal Stochastic Control Laws , 1971 .

[5] Harold J. Kushner,et al. Existence results for optimal stochastic controls , 1975 .

[6] A. Balakrishnan. Applied Functional Analysis , 1976 .

[7] J. Bismut,et al. Théorie probabiliste du contrôle des diffusions , 1976 .

[8] A. Veretennikov. ON STRONG SOLUTIONS AND EXPLICIT FORMULAS FOR SOLUTIONS OF STOCHASTIC INTEGRAL EQUATIONS , 1981 .

[9] L. Rogers. Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[10] U. Haussmann. Existence of optimal markovian controls for degenerate diffusions , 1986 .

[11] KarouiNicole El,et al. Compactification methods in the control of degenerate diffusions: existence of an optimal control , 1987 .

[12] Harold J. Kushner,et al. Nearly optimal state feedback controls for stochastic systems with wideband noise disturbances , 1987 .

[13] V. Borkar. The probabilistic structure of controlled diffusion processes , 1988 .