000			02926nam a22002057a 4500
005			20220729134239.0
008			220729b |||||||| |||| 00| 0 eng d
020			_a9789814740302
040			_aS.X.U.K
041			_aEnglish
082			_aR 519.23 CHE(INT)
100			_aChen, Mu-Fa
245			_aIntroduction to stochastic processes _cMu-Fa Chen, Yong-Hua Mao
260			_aBeijing _bHigher education press _bWorld scientific _cc2021
300			_a230p _bH.B.
440			_aWorld scientific series on probability theory and applications V.2
500			_aCover Page Title Page Copyright Page Preface to the English Edition Preface to the Chinese Edition Contents Markov Processes 1. Discrete-Time Markov Chains 1.1 Stochastic Models for Economic Optimization and Markov Chains 1.2 Discrete-Time Markov Chains. Recurrence and Ergodicity 1.3 Limit Theorems in General Situation 1.4 Criteria. The Minimal Nonnegative Solution 1.5 Some Typical Discrete-Time Markov Chains 1.6 Supplements and Exercises 2. Continuous-Time Markov Chains 2.1 Continuous-Time Markov Chains. Uniqueness 2.2 Recurrence and Ergodicity 2.3 Single Birth Processes and Birth-Death Processes 2.4 Branching Processes and Extended Branching Processes 2.5 Supplements and Exercises 3. Reversible Markov Chains 3.1 Reversible and Symmetrizable Markov Chains 3.2 Estimate of Spectral Gap 3.3 Appendix: Spectral Representation of Reversible Markov Chains 3.4 Supplements and Exercises 4. General Markov Processes 4.1 Markov Property and Its Equivalence 4.2 Strong Markov Property 4.3 Appendix: Optimal Stopping Problem—The Secretary Problem 4.4 Supplements and Exercises Stochastic Analysis 5. Martingale 5.1 Definitions and Basic Properties 5.2 Doob’s Stopping Theorem 5.3 Fundamental Inequalities 5.4 Convergence Theorems 5.5 Continuous-Time (Sub/Super) Martingale 5.6 Two Applications of Martingale Theory 5.7 Supplements and Exercises 6. Brownian Motion 6.1 Brownian Motion 6.2 The Trajectory Property 6.3 Martingale Property of Brownian Motion 6.4 Multi-Dimensional Brownian Motion 6.5 Supplements and Exercises 7. Stochastic Integral and Diffusion Processes 7.1 Stochastic Integral 7.2 Itô’s Formula 7.3 Stochastic Differential Equation (SDE) (Dimension One) 7.4 One-Dimensional Diffusion Process 7.5 Supplements and Exercises 8. Semimartingale and Stochastic Integral 8.1 Uniqueness of Doob-Meyer Decomposition 8.2 Existence of Doob-Meyer Decomposition 8.3 Properties of Variation Processes 8.4 Stochastic Integral 8.5 Itô’s Formula 8.6 Local Martingale and Semimartingale 8.7 Multivariate Stochastic Integral 8.8 Stochastic Differential Equation (Multidimension) 8.9 Feynman-Kac Formula, Random Change of Time, and Girsanov’s Theorem 8.10 Supplements and Exercises Notes Bibliography Index
650			_aPROBABILITIES _aAPPLIED MATHEMATICS _aSTOCHASTIC PROCESS
942			_cUS
999			_c7195 _d7195