000			02628nam a22002177a 4500
005			20250103183408.0
008			250103b |||||||| |||| 00| 0 eng d
020			_a9781944660512
082			_a519.1 _bCHE
100			_aChen, Mu-Fa _920106
245			_aIntroduction to stochastic processes
260			_bWorld Scientific Publishing _aSingapore _c2023
300			_axiii, 230 p.
365			_aINR _b1295.00
490			_aWorld Scientific Series on Probability Theory and Its Applications : Vol. 2
520			_aThe 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. (https://www.worldscientific.com/worldscibooks/10.1142/9903?srsltid=AfmBOoopnAMqYIUW_LQCMrB_jOj2gx530T5QcLQdJvYMKCeLdPYKmm1i#t=aboutBook)
650			_aStochastic processes _9814
650			_aMarkov renewal theory _920107
700			_aMao, Yong-Hua _920108
942			_cBK _2ddc
999			_c7759 _d7759