markov chains north holland mathematical library

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Markov Chains

Author : D. Revuz
ISBN : 0080880223
Genre : Mathematics
File Size : 56. 88 MB
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This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail. The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.

Markov Processes Feller Semigroups And Evolution Equations

Author : J. A. van Casteren
ISBN : 9789814322188
Genre : Mathematics
File Size : 86. 78 MB
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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.

Probability Theory

Author : Achim Klenke
ISBN : 9781447153610
Genre : Mathematics
File Size : 79. 81 MB
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This second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including: • limit theorems for sums of random variables • martingales • percolation • Markov chains and electrical networks • construction of stochastic processes • Poisson point process and infinite divisibility • large deviation principles and statistical physics • Brownian motion • stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.

Operator Theory Operator Algebras And Applications

Author : Alejandro D. de Acosta
ISBN : 9780821890899
Genre : Mathematics
File Size : 40. 72 MB
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Metastability And Markov State Models In Molecular Dynamics Modeling Analysis Algorithmic Approaches

Author : Christof Schütte
ISBN : 9780821843598
Genre : Mathematics
File Size : 39. 72 MB
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Applications in modern biotechnology and molecular medicine often require simulation of biomolecular systems in atomic representation with immense length and timescales that are far beyond the capacity of computer power currently available. As a consequence, there is an increasing need for reduced models that describe the relevant dynamical properties while at the same time being less complex. In this book the authors exploit the existence of metastable sets for constructing such a reduced molecular dynamics model, the so-called Markov state model (MSM), with good approximation properties on the long timescales. With its many examples and illustrations, this book is addressed to graduate students, mathematicians, and practical computational scientists wanting an overview of the mathematical background for the ever-increasing research activity on how to construct MSMs for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecular sensors to molecular aggregation. This book bridges the gap between mathematical research on molecular dynamics and its practical use for realistic molecular systems by providing readers with tools for performing in-depth analysis of simulation and data-analysis methods. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Quasi Stationary Phenomena In Nonlinearly Perturbed Stochastic Systems

Author : Mats Gyllenberg
ISBN : 9783110208252
Genre : Mathematics
File Size : 47. 42 MB
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This book is devoted to the mathematical studies of stochastic systems with quasi-stationary phenomena which have applications to population dynamics or epidemic models. In addition to its use for the research and reference purposes, the book can also be used in special courses on the subject and as a complementary reading in general courses on stochastic processes. In this respect, it may be useful for specialists as well as doctoral and advanced undergraduate students.

Martingales And Markov Chains

Author : Paolo Baldi
ISBN : 9781482285918
Genre : Mathematics
File Size : 49. 30 MB
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A thorough grounding in Markov chains and martingales is essential in dealing with many problems in applied probability, and is a gateway to the more complex situations encountered in the study of stochastic processes. Exercises are a fundamental and valuable training tool that deepen students' understanding of theoretical principles and prepare them to tackle real problems. In addition to a quick but thorough exposition of the theory, Martingales and Markov Chains: Solved Exercises and Elements of Theory presents, more than 100 exercises related to martingales and Markov chains with a countable state space, each with a full and detailed solution. The authors begin with a review of the basic notions of conditional expectations and stochastic processes, then set the stage for each set of exercises by recalling the relevant elements of the theory. The exercises range in difficulty from the elementary, requiring use of the basic theory, to the more advanced, which challenge the reader's initiative. Each section also contains a set of problems that open the door to specific applications. Designed for senior undergraduate- and graduate level students, this text goes well beyond merely offering hints for solving the exercises, but it is much more than just a solutions manual. Within its solutions, it provides frequent references to the relevant theory, proposes alternative ways of approaching the problem, and discusses and compares the arguments involved.

Analysis And Probability

Author : Palle E. T. Jorgensen
ISBN : 9780387295190
Genre : Mathematics
File Size : 54. 2 MB
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Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature

Nonlinearly Perturbed Semi Markov Processes

Author : Dmitrii Silvestrov
ISBN : 9783319609881
Genre : Mathematics
File Size : 64. 18 MB
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The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come.

Bulletin Of The American Mathematical Society

Author :
ISBN : UOM:49015003188381
Genre : Mathematics
File Size : 60. 45 MB
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