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Autore: | Mamontov Yevgeny <1955-> |
Titolo: | High-dimensional nonlinear diffusion stochastic processes : modelling for engineering applications / / Yevgeny Mamontov, Magnus Willander |
Pubblicazione: | Singapore ; ; River Edge, NJ, : World Scientific, 2001 |
Edizione: | 1st ed. |
Descrizione fisica: | 1 online resource (322 p.) |
Disciplina: | 519.23 |
Soggetto topico: | Engineering - Mathematical models |
Stochastic processes | |
Diffusion processes | |
Differential equations, Nonlinear | |
Altri autori: | WillanderM |
Note generali: | Description based upon print version of record. |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | Contents ; Preface ; Chapter 1 Introductory Chapter ; 1.1 Prerequisites for Reading ; 1.2 Random Variable. Stochastic Process. Random Field. High-Dimensional Process. One-Point Process |
1.3 Two-Point Process. Expectation. Markov Process. Example of Non-Markov Process Associated with Multidimensional Markov Process 1.4 Preceding Subsequent and Transition Probability Densities. The Chapman-Kolmogorov Equation. Initial Condition for Markov Process | |
1.4.1 The Chapman-Kolmogorov equation 1.4.2 Initial condition for Markov process ; 1.5 Homogeneous Markov Process. Example of Markov Process: The Wiener Process ; 1.6 Expectation Variance and Standard Deviations of Markov Process | |
1.7 Invariant and Stationary Markov Processes. Covariance. Spectral Densities 1.8 Diffusion Process ; 1.9 Example of Diffusion Processes: Solutions of Ito's Stochastic Ordinary Differential Equation ; 1.10 The Kolmogorov Backward Equation | |
1.11 Figures of Merit. Diffusion Modelling of High-Dimensional Systems 1.12 Common Analytical Techniques to Determine Probability Densities of Diffusion Processes. The Kolmogorov Forward Equation ; 1.12.1 Probability density ; 1.12.2 Invariant probability density | |
1.12.3 Stationary probability density | |
Sommario/riassunto: | This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs). The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficie |
Titolo autorizzato: | High-dimensional nonlinear diffusion stochastic processes |
ISBN: | 1-281-95622-8 |
9786611956226 | |
981-281-054-4 | |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910826713703321 |
Lo trovi qui: | Univ. Federico II |
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