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Author Muldowney, P. (Patrick), 1946-

Title A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration / Patrick Muldowney
Published Hoboken, N.J. : Wiley, 2012

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Description 1 online resource
Contents 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×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
Summary "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 random variation"-- Provided by publisher
Bibliography Includes bibliographical references and index
Notes Print version record and CIP data provided by publisher
Subject Random variables.
Calculus of variations.
Path integrals.
Mathematical analysis.
MATHEMATICS -- Mathematical Analysis.
Calculus of variations
Mathematical analysis
Path integrals
Random variables
Form Electronic book
LC no. 2012008712
ISBN 9781118345948
1118345940
9781118345924
1118345924
9781118345931
1118345932
9781118345955
1118345959
111816640X
9781118166406
1283835002
9781283835008