Introduction to Stochastic Processes

Paul G Hoel

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Sprache: Englisch

Verlag: Houghton Mifflin, 1972

0395120764 / 9780395120767

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The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts -- Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.…

Bestandsnummer des Verkäufers CIN0395120764G

Bibliografische Details

Titel
Introduction to Stochastic Processes
Autor
Paul G Hoel
Verlag
Houghton Mifflin
Erscheinungsjahr
1972
Zustand
Good
Einband
Hardback
Sprache
Englisch
ISBN-10
0395120764
ISBN-13
9780395120767

World of Books (was SecondSale)

Montgomery, IL, USA

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AbeBooks-Verkäufer/-in seit 20. Dezember 2007

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