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Stochastic Growth Equations : Mathematics and Modeling.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Newark :
John Wiley & Sons, Incorporated,
2017.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1.10 Set and Measure Functions1.10.1 Set Functions; 1.10.2 Measure Functions; 1.10.3 Outer Measure Functions; 1.10.4 Complete Measure Functions; 1.10.5 Lebesgue Measure; 1.10.6 Measurable Functions; 1.10.7 Lebesgue Measurable Functions; 1.11 Normed Linear Spaces; 1.11.1 Space of Bounded Real-Valued Functions; 1.11.2 Space of Bounded Continuous Real-Valued Functions; 1.11.3 Some Classical Banach Spaces; 1.12 Integration; 1.12.1 Integral of a Non-negative Simple Function; 1.12.2 Integral of a Non-negative Measurable Function Using Simple Functions; 1.12.3 Integral of a Measurable Function.
- 1.12.4 Integral of a Measurable Function on a Measurable Set1.12.5 Convergence of Sequences of Functions; Chapter 2 Mathematical Foundations 2: Probability, Random Variables, and Convergence of Random Variables; 2.1 Probability Spaces; 2.2 Probability Distributions; 2.3 The Expectation of a Random Variable; 2.3.1 Theoretical Underpinnings; 2.3.2 Computational Considerations; 2.4 Moments of a Random Variable; 2.5 Multiple Random Variables; 2.5.1 The Discrete Case; 2.5.2 The Continuous Case; 2.5.3 Expectations and Moments; 2.5.4 The Multivariate Discrete and Continuous Cases.
- 2.6 Convergence of Sequences of Random Variables2.6.1 Almost Sure Convergence; 2.6.2 Convergence in Lp, p>0; 2.6.3 Convergence in Probability; 2.6.4 Convergence in Distribution; 2.6.5 Convergence of Expectations; 2.6.6 Convergence of Sequences of Events; 2.6.7 Applications of Convergence of Random Variables; 2.7 A Couple of Important Inequalities; Appendix 2.A The Conditional Expectation E(X|Y); Chapter 3 Mathematical Foundations 3: Stochastic Processes, Martingales, and Brownian Motion; 3.1 Stochastic Processes; 3.1.1 Finite-Dimensional Distributions of a Stochastic Process.
- 3.1.2 Selected Characteristics of Stochastic Processes3.1.3 Filtrations of A; 3.2 Martingales; 3.2.1 Discrete-Time Martingales; 3.2.1.1 Discrete-Time Martingale Convergence; 3.2.2 Continuous-Time Martingales; 3.2.2.1 Continuous-Time Martingale Convergence; 3.2.3 Martingale Inequalities; 3.3 Path Regularity of Stochastic Processes; 3.4 Symmetric Random Walk; 3.5 Brownian Motion; 3.5.1 Standard Brownian Motion; 3.5.2 BM as a Markov Process; 3.5.3 Constructing BM; 3.5.3.1 BM Constructed from N(0, 1) Random Variables; 3.5.3.2 BM as the Limit of Symmetric Random Walks; 3.5.4 White Noise Process.