## Optimal control of diffusion processes |

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### Contents

Compactness of laws | 23 |

Dynamic programming | 53 |

The degenerate case | 84 |

Copyright | |

4 other sections not shown

### Common terms and phrases

absolutely continuous applications arbitrary Cb(Rd claim follows compact conclude continuous with respect Control Optim controlled diffusion convergence Corollary 1.1 corresponding solution defined denote diffusion processes Dirac measure dynamic programming e-optimal e"at existence of optimal feedback control hence HJB equation infimum initial condition initial data Lebesgue measure Lemma limit point llarkov Markov process martingale natural filtration near-monotonicity Nisio nondegenerate Nonlinear partial differential optimal control P.L. Lions P(Rd partial differential equations partial observations precise control probability measure probability space Proof Let proof of Theorem prove replaced resp S.R.S. Varadhan satisfying I.1.1 semigroup separated control problem solution of I.1.1 Springer stationary Markov control stochastic control Stochastic differential equations subset t e 0,T Theorem 1.1 theory topology unique solution V.S. Borkar viscosity solution wide-sense admissible controls Wiener process