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1.

電子ブック
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1. Random Walk, Brownian Motion, and Martingales. 1st ed. 2021
by Rabi Bhattacharya, Edward C. Waymire
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: Graduate Texts in Mathematics ; 292
オンライン: https://doi.org/10.1007/978-3-030-78939-8
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目次情報: 続きを見る
1. What is a Stochastic Process?
2. The Simple Random Walk I: Associated Boundary Value Distributions, Transience and Recurrence
3. The Simple Random Walk II: First Passage Times
4. Multidimensional Random Walk
5. The Poisson Process, Compound Poisson Process, and Poisson Random Field
6. The Kolmogorov–Chentsov Theorem and Sample Path Regularity
7. Random Walk, Brownian Motion and the Strong Markov Property
8. Coupling Methods for Markov Chains and the Renewal Theorem for Lattice Distributions
9. Bienyamé–Galton–Watson Simple Branching Process and Extinction
10. Martingales: Definitions and Examples
11. Optional Stopping of (Sub)Martingales
12. The Upcrossings Inequality and (Sub)Martingale Convergence
13
Continuous Parameter Martingales
14. Growth of Supercritical Bienyamé–Galton–Watson Simple Branching Processes
15. Stochastic Calculus for Point Processes and a Martingale Characterization of the Poisson Process
16. First Passage Time Distributions for Brownian Motion with Drift and a Local Limit Theorem
17. The Functional Central Limit Theorem (FCLT)
18. ArcSine Law Asymptotics
19. Brownian Motion on the Half-Line: Absorption and Reflection
20. The Brownian Bridge
21. Special Topic: Branching Random Walk, Polymers and Multiplicative Cascades
22. Special Topic: Bienyamé–Galton–Watson Simple Branching Process and Excursions
23. Special Topic: The Geometric Random Walk and the Binomial Tree Model of Mathematical Finance
24. Special Topic: Optimal Stopping Rules
25. Special Topic: A Comprehensive Renewal Theory for General Random Walks
26. Special Topic: Ruin Problems in Insurance
27. Special Topic: Fractional Brownian Motion and/or Trends: The Hurst Effect
28. Special Topic: Incompressible Navier–Stokes Equations and the LeJan–Sznitman Cascade
References
Related Textbooks and Monographs
Symbol Definition List
Name Index
Index
1. What is a Stochastic Process?
2. The Simple Random Walk I: Associated Boundary Value Distributions, Transience and Recurrence
3. The Simple Random Walk II: First Passage Times
2.

電子ブック
ＥＢ
2. Stationary Processes and Discrete Parameter Markov Processes. 1st ed. 2022
by Rabi Bhattacharya, Edward C. Waymire
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2022
シリーズ名: Graduate Texts in Mathematics ; 293
オンライン: https://doi.org/10.1007/978-3-031-00943-3
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目次情報: 続きを見る
Symbol Definition List
1. Fourier Analysis: A Brief
2. Weakly Stationary Processes and their Spectral Measures
3. Spectral Representation of Stationary Processes
4. Birkhoff’s Ergodic Theorem
5. Subadditive Ergodic Theory
6. An Introduction to Dynamical Systems
7. Markov Chains
8. Markov Processes with General State Space
9. Stopping Times and the Strong Markov Property
10. Transience and Recurrence of Markov Chains
11. Birth–Death Chains
12. Hitting Probabilities & Absorption
13. Law of Large Numbers and Invariant Probability for Markov Chains by Renewal Decomposition
14. The Central Limit Theorem for Markov Chains by Renewal Decomposition
15. Martingale Central Limit Theorem
16. Stationary Ergodic Markov Processes: SLLN & FCLT
17. Linear Markov Processes
18. Markov Processes Generated by Iterations of I.I.D. Maps
19. A Splitting Condition and Geometric Rates of Convergence to Equilibrium
20. Irreducibility and Harris Recurrent Markov Processes
21. An Extended Perron–Frobenius Theorem and Large Deviation Theory for Markov Processes
22. Special Topic: Applications of Large Deviation Theory
23. Special Topic: Associated Random Fields, Positive Dependence, FKG Inequalities
24. Special Topic: More on Coupling Methods and Applications
25. Special Topic: An Introduction to Kalman Filter
A. Spectral Theorem for Compact Self-Adjoint Operators and Mercer’s Theorem
B. Spectral Theorem for Bounded Self-Adjoint Operators
C. Borel Equivalence for Polish Spaces
D. Hahn–Banach, Separation, and Representation Theorems in Functional Analysis
References
Author Index
Subject Index
Symbol Definition List
1. Fourier Analysis: A Brief
2. Weakly Stationary Processes and their Spectral Measures