## High-dimensional Nonlinear Diffusion Stochastic Processes: Modelling for Engineering Applications (Google eBook)Annotation This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations.The book presents the new analytical treatment which can serve as the basis of a combined, analytical -- numerical approach to greater computational efficiency. Some examples of the modelling of noise in semiconductor devices are provided |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 | |

Diffusion Processes | 63 |

Invariant Diffusion Processes | 85 |

Stationary Diffusion Processes | 107 |

Itos Stochastic Partial Differential | 141 |

Itos Stochastic Partial Differential | 163 |

Distinguishing Features | 197 |

### Common terms and phrases

analytical analytical-numerical approach Appendix approximation Arnold assertion assumption asymptotic Banach spaces basis Bellomo Chapter computational considered corresponding covariance Definition Demir dependence derivatives described determined deterministic differential equations diffusion functions domain Q drift and diffusion drift function elementary event engineering entries evaluate example expression feature fluid formula function g holds independent initial condition initial-value problem instance integral ISODE system ISPDE ISPIDE Ito's stochastic Lebesgue integral linear macroscopic Mamontov and Willander Markov process mathematical matrix H(t,x means method momentum-relaxation noise nonlinear Note ODE system parameter particle physical present book probability density quantity random variable Remark respect right-hand side scalar semiconductor SF-ISPDE Soize solution specific spectral density stationary DSP Stochastic Differential Equations stochastic process stochastic resonance t_<tt t>to techniques Theorem 2.1 theory tion transition probability density treatment uniformly valid variance matrix velocity well-known Wiener process