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040 _aWSPC
_beng
_cWSPC
020 _a9789814740319
_q(ebook)
020 _a9814740314
_q(ebook)
020 _z9814740306
_q(hbk.)
020 _z9789814740302
_q(hbk.)
050 0 0 _aQA274
_b.C446 2021
072 7 _aMAT
_x029040
_2bisacsh
072 7 _aMAT
_x007000
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_x005000
_2bisacsh
082 0 0 _a519.2/3
_223
049 _aMAIN
100 1 _aChen, Mu-Fa.
_920786
245 1 0 _aIntroduction to stochastic processes
_h[electronic resource] /
_cMu-Fa Chen and Yong-Hua Mao.
260 _aSingapore :
_bWorld Scientific,
_c2021.
300 _a1 online resource (244 p.).
490 1 _aWorld Scientific series on probability theory and its applications ;
_vVol. 2
504 _aIncludes bibliographical references and index.
505 0 _aPreface to the English edition -- Preface to the Chinese edition -- Markov processes. Discrete-time Markov chains -- Continuous-time Markov chains -- Reversible Markov chains -- General Markov processes -- Stochastic analysis. Martingale --Brownian motion -- stochastic integral and diffusion processes -- Semimartingale and stochastic integral - Notes - Bibliography - Index.
520 _a"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"--Publisher's website.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat reader.
650 0 _aStochastic processes.
_93246
655 0 _aElectronic books.
_93294
700 1 _aMao, Yong-Hua.
_920787
830 0 _aWorld Scientific series on probability theory and its applications ;
_vVol. 2.
_920788
856 4 0 _uhttps://www.worldscientific.com/worldscibooks/10.1142/9903#t=toc
_zAccess to full text is restricted to subscribers.
942 _cEBK
999 _c72637
_d72637