[PDF] Markov Processes Feller Semigroups And Evolution Equations eBook

Author : Jan A Van Casteren
Publisher : World Scientific
Page : 825 pages
File Size : 22,56 MB
Release : 2010-11-25
Category : Mathematics
ISBN : 9814464171

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The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.

Author : J. A. van Casteren
Publisher : World Scientific
Page : 825 pages
File Size : 19,28 MB
Release : 2011
Category : Mathematics
ISBN : 9814322180

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The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.

Author : Vassili N. Kolokoltsov
Publisher : Walter de Gruyter
Page : 449 pages
File Size : 46,25 MB
Release : 2011
Category : Mathematics
ISBN : 3110250101

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This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for

Author : Adam Bobrowski
Publisher : Cambridge University Press
Page : 279 pages
File Size : 43,43 MB
Release : 2020-11-26
Category : Mathematics
ISBN : 1108495796

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A clear explanation of what an explosive Markov chain does after it passes through all available states in finite time.

Author : Vassili N. Kolokoltsov
Publisher : Walter de Gruyter
Page : 449 pages
File Size : 26,3 MB
Release : 2011-03-29
Category : Mathematics
ISBN : 311025011X

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Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space. This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools. The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes. From the contents: Tools from Probability and Analysis Brownian motion Markov processes and martingales SDE, ψDE and martingale problems Processes in Euclidean spaces Processes in domains with a boundary Heat kernels for stable-like processes Continuous-time random walks and fractional dynamics Complex chains and Feynman integral

Author : Stewart N. Ethier
Publisher : John Wiley & Sons
Page : 552 pages
File Size : 19,13 MB
Release : 1986-04-04
Category : Mathematics
ISBN :

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As a graduate text/reference on Markov Processes and their relationship to operator semigroups, this book presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation.

Author : Rabi Bhattacharya
Publisher : Springer Nature
Page : 502 pages
File Size : 35,15 MB
Release : 2023-11-16
Category : Mathematics
ISBN : 3031332962

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This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples. After a review of some background material, the reader is introduced to semigroup theory, including the Hille–Yosida Theorem, used to construct continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Feller’s seminal theory of the most general one-dimensional diffusions studied in a later chapter. This is followed by two chapters with probabilistic constructions of jump Markov processes, and processes with independent increments, or Lévy processes. The greater part of the book is devoted to Itô’s fascinating theory of stochastic differential equations, and to the study of asymptotic properties of diffusions in all dimensions, such as explosion, transience, recurrence, existence of steady states, and the speed of convergence to equilibrium. A broadly applicable functional central limit theorem for ergodic Markov processes is presented with important examples. Intimate connections between diffusions and linear second order elliptic and parabolic partial differential equations are laid out in two chapters, and are used for computational purposes. Among Special Topics chapters, two study anomalous diffusions: one on skew Brownian motion, and the other on an intriguing multi-phase homogenization of solute transport in porous media.

Author : Tomasz R. Bielecki
Publisher : Cambridge University Press
Page : 280 pages
File Size : 28,57 MB
Release : 2020-08-27
Category : Mathematics
ISBN : 1108895379

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The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.

Author : Daniel T. Gillespie
Publisher : Gulf Professional Publishing
Page : 600 pages
File Size : 16,48 MB
Release : 1992
Category : Mathematics
ISBN : 9780122839559

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Markov process theory provides a mathematical framework for analyzing the elements of randomness that are involved in most real-world dynamical processes. This introductory text, which requires an understanding of ordinary calculus, develops the concepts and results of random variable theory.

Author : Kazuaki Taira
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 25,65 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 3662098571

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This volume will be of great appeal to both advanced students and researchers. For the former, it serves as an effective introduction to three interrelated subjects of analysis: semigroups, Markov processes and elliptic boundary value problems. For the latter, it provides a new method for the analysis of Markov processes, a powerful method clearly capable of extensive further development.