Introduction to stochastic processes
Mu-Fa Chen, Yong-Hua Mao
- Beijing Higher education press World scientific c2021
- 230p H.B.
- World scientific series on probability theory and applications V.2 .
Cover 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
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PROBABILITIES APPLIED MATHEMATICS STOCHASTIC PROCESS