An investigation of the logical foundations of the theory behind Markov random processes, this text explores subprocesses, transition functions, and conditions for boundedness and continuity. Rather than focusing on probability measures individually, the work explores connections between functions. An elementary grasp of the theory of Markov processes is assumed. 1961 edition.
This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also
A self-contained treatment, this text covers both theory and applications. Topics include homogeneous finite and infinite Markov chains, including those employed in the mathematical modeling of psycho
This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing
These notes are based on a series of lectures delivered at the Scuola Normale Superiore in March 1986. They are intended to explore some connections between the theory of control of Markov stochastic
This invaluable book provides approximately eighty examples illustrating the theory of controlled discrete-time Markov processes. Except for applications of the theory to real-life problems like stock
The theory of Markov decision processes focuses on controlled Markov chains in discrete time. The authors establish the theory for general state and action spaces and at the same time show its applica
Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly importa
This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mat
This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another termi- nology multistage Markovian decision proce
Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and t
This graduate-level text explores the relationship between Markov processes and potential theory, in addition to aspects of the theory of additive functionals. Topics include Markov processes, excessi
At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten- sion of probability theory, allows the modeling of the evolution of systems through the
This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
This book presents an algebraic development of the theory of countable state space Markov chains with discrete- and continuous-time parameters. A Markov chain is a stochastic process characterized by
After reviewing essentials of analysis, including functional analysis, convexity, distribution theory, and interpolation theory, this book treats Fourier analysis and one-parameter operator semigroups
Kiyosi Ito's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geo
This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum and then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original,
This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum and then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original,
