## Stochastic Differential Equations |

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### Contents

Some Problems and Methods for the Analysis of Stochastic | 21 |

Wave Propagation and Conductivity in Random Media | 35 |

Analysis of Some Stochastic Ordinary Differential Equations | 97 |

Optimal Control of Diffusion Processes | 163 |

Optimal Control of a Partially Observed Stochastic System | 173 |

Building and Evaluating Nonlinear Filters | 189 |

### Common terms and phrases

adapted Appl applied approximation assume asymptotic average bounded bump calculation coefficients conductivity consider constant continuous correlation functions corresponding coupling defined denote density depend derived determined diffusion discussed distribution energy evaluated exact results example existence expected expression Figure first-order fixed fluctuations follows formula function Gaussian given gives Hence impurity independent initial conditions integral interest interval limit linear Markov Math Mathematical matrix mean measurable method Note observations obtained one-dimensional operator partial perturbation Phys positive potential presentation probability problem proof propagation random refer relation satisfies scattering second-order moments shown simple solution solved space stationary statistics stochastic differential equation theorem theory tion transforms transition unit variable vector vesicle wave white noise yields York zero