High-dimensional nonlinear diffusion stochastic processes [[electronic resource] ] : modelling for engineering applications / / Yevgeny Mamontov, Magnus Willander

• Autore: Mamontov Yevgeny <1955->
• Pubblicazione: Singapore ; ; River Edge, NJ, : World Scientific, 2001
• 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
• Serie: Series on advances in mathematics for applied sciences ; ; 56.