## Theory and Applications of Stochastic Differential EquationsPresents theory, sources, and applications of stochastic differential equations of Ito's type; those containing white noise. Closely studies first passage problems by modern singular perturbation methods and their role in various fields of science. Introduces analytical methods to obtain information on probabilistic quantities. Demonstrates the role of partial differential equations in this context. Clarifies the relationship between the complex mathematical theories involved and sources of the problem for physicists, chemists, engineers, and other non-mathematical specialists. |

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### Contents

Review of Probability Theory | 1 |

The Stochastic Itô Calculus | 61 |

3 | 77 |

Copyright | |

8 other sections not shown

### Common terms and phrases

approximation assume asymptotic atomic backward barrier boundary bounded Brownian motion called Chapter characteristic coefficient collisions compute Consider constant construct contains continuous converges coordinates corresponding crystal defined denote density Derive described determined diffusion directions distribution dw(s dw(t elementary elements equal equilibrium example EXERCISE exists exit expansion expected field Figure filter Find finite Fokker-Planck follows force formula frequency function Gaussian given hence independent initial integral interval layer leading term limit linear mathematical matrix mean measure molecules noise normal observed obtain occurs operator origin particle physical positive potential probability problem properties random variable reaction reduced represents respect result satisfies Schuss sequence Show shown signal smooth solution space stable stochastic differential equation takes theorem theory tion transition vector Write zero