Introduction to stochastic processes Mu-Fa Chen, Yong-Hua Mao
Material type:
TextLanguage: English Series: World scientific series on probability theory and applications V.2Publication details: Beijing Higher education press World scientific c2021Description: 230p H.BISBN: - 9789814740302
- R 519.23 CHE(INT)
| Item type | Current library | Collection | Call number | Vol info | Copy number | Status | Barcode | |
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REFERENCE STATISTICS
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St. Xavier's University, Kolkata Reference Section | Reference | R 519.23 CHE(INT) (Browse shelf(Opens below)) | S.X.U.K | 6934 | Not For Loan | US6934 |
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| R 519.2 ROS(SIM)Ed6 Simulation / | R 519.23 BHA(STO) Stochastic processes with applications | R 519.23 BHA(STO)C1 Stochastic processes with applications | R 519.23 CHE(INT) Introduction to stochastic processes | R 519.24 MUL.Ed8 Multivariate Data Analysis | R 519.3 DIX(GAM) Ed3 Games of strategy | R 519.3 FER(GAM) Game theory : an applied introduction |
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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