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A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration /
"This book presents a self-contained study of the Riemann approach to the theory of random variation and assumes only some familiarity with probability or statistical analysis, basic Riemann integration, and mathematical proofs. The author focuses on non-absolute convergence in conjunction with...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, N.J. :
Wiley,
2012.
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| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- A Modern Theory of Random Variation: With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration; Contents; Preface; Symbols; 1 Prologue; 1.1 About This Book; 1.2 About the Concepts; 1.3 About the Notation; 1.4 Riemann, Stieltjes, and Burkill Integrals; 1.5 The -Complete Integrals; 1.6 Riemann Sums in Statistical Calculation; 1.7 Random Variability; 1.8 Contingent and Elementary Forms; 1.9 Comparison With Axiomatic Theory; 1.10 What Is Probability?; 1.11 Joint Variability; 1.12 Independence; 1.13 Stochastic Processes; 2 Introduction.
- 2.1 Riemann Sums in Integration2.2 The -Complete Integrals in Domain]0,1]; 2.3 Divisibility of the Domain]0,1]; 2.4 Fundamental Theorem of Calculus; 2.5 What Is Integrability?; 2.6 Riemann Sums and Random Variability; 2.7 How to Integrate a Function; 2.8 Extension of the Lebesgue Integral; 2.9 Riemann Sums in Basic Probability; 2.10 Variation and Outer Measure; 2.11 Outer Measure and Variation in [0,1]; 2.12 The Henstock Lemma; 2.13 Unbounded Sample Spaces; 2.14 Cauchy Extension of the Riemann Integral; 2.15 Integrability on]0, (infinity)[; 2.16 ""Negative Probability""
- 4.7 Variation of a Function4.8 Variation and Integral; 4.9 Rt{u00D7}N(T)-Variation; 4.10 Introduction to Fubini's Theorem; 4.11 Fubini's Theorem; 4.12 Limits of Integrals; 4.13 Limits of Non-Absolute Integrals; 4.14 Non-Integrable Functions; 4.15 Conclusion; 5 Random Variability; 5.1 Measurability of Sets; 5.2 Measurability of Random Variables; 5.3 Representation of Observables; 5.4 Basic Properties of Random Variables; 5.5 Inequalities for Random Variables; 5.6 Joint Random Variability; 5.7 Two or More Joint Observables; 5.8 Independence in Random Variability; 5.9 Laws of Large Numbers.
- 5.10 Introduction to Central Limit Theorem5.11 Proof of Central Limit Theorem; 5.12 Probability Symbols; 5.13 Measurability and Probability; 5.14 The Calculus of Probabilities; 6 Gaussian Integrals; 6.1 Fresnel's Integral; 6.2 Evaluation of Fresnel's Integral; 6.3 Fresnel's Integral in Finite Dimensions; 6.4 Fresnel Distribution Function in Rn; 6.5 Infinite-Dimensional Fresnel Integral; 6.6 Integrability on Rt; 6.7 The Fresnel Function Is Vbg*; 6.8 Incremental Fresnel Integral; 6.9 Fresnel Continuity Properties; 7 Brownian Motion; 7.1 c-Brownian Motion; 7.2 Brownian Motion With Drift.