High-dimensional Nonlinear Diffusion Stochastic Processes: Modelling for Engineering Applications (Google eBook)

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World Scientific, Jan 1, 2001 - Mathematics - 297 pages
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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
  

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Contents

Introductory Chapter
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
Proofs of the Theorems in Chapter 2
231
Appendix E Proofs of the Theorems in Chapter 4
243
Eigenvalues and Eigenfunctions
255
Appendix H Resources for Engineering Parallel
261
Index
281
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