04953nam 2200733Ia 450 991045438390332120200520144314.01-281-95622-89786611956226981-281-054-4(CKB)1000000000538091(EBL)1679503(OCoLC)879074242(SSID)ssj0000170956(PQKBManifestationID)11155899(PQKBTitleCode)TC0000170956(PQKBWorkID)10235853(PQKB)11276576(MiAaPQ)EBC1679503(WSP)00004494(Au-PeEL)EBL1679503(CaPaEBR)ebr10255985(CaONFJC)MIL195622(EXLCZ)99100000000053809120001101d2001 uy 0engur|n|---|||||txtccrHigh-dimensional nonlinear diffusion stochastic processes[electronic resource] modelling for engineering applications /Yevgeny Mamontov, Magnus WillanderSingapore ;River Edge, NJ World Scientific20011 online resource (322 p.)Series on advances in mathematics for applied sciences ;56Description based upon print version of record.981-02-4385-5 Includes bibliographical references and index.Contents ; Preface ; Chapter 1 Introductory Chapter ; 1.1 Prerequisites for Reading ; 1.2 Random Variable. Stochastic Process. Random Field. High-Dimensional Process. One-Point Process1.3 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 Process1.4.1 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 Process1.7 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 Equation1.11 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 density1.12.3 Stationary probability density 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 efficieSeries on advances in mathematics for applied sciences ;56.EngineeringMathematical modelsStochastic processesDiffusion processesDifferential equations, NonlinearElectronic books.EngineeringMathematical models.Stochastic processes.Diffusion processes.Differential equations, Nonlinear.519.23Mamontov Yevgeny1955-980633Willander M980634MiAaPQMiAaPQMiAaPQBOOK9910454383903321High-dimensional nonlinear diffusion stochastic processes2237464UNINA