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The Resource A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration, Patrick Muldowney

A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration, Patrick Muldowney

Creator
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"--
Language
eng
Work
Publication
Extent
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{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
Isbn
9781118166406
Instance
Label
A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration
Title
A modern theory of random variation
Title remainder
with applications in stochastic calculus, financial mathematics, and Feynman integration
Statement of responsibility
Patrick Muldowney
Creator
Subject
Language
eng
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"--
Member of
Assigning source
Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorDate
1946-
http://library.link/vocab/creatorName
Muldowney, P.
Dewey number
519.2/3
Index
index present
LC call number
QA273
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Random variables
  • Calculus of variations
  • Path integrals
  • Mathematical analysis
  • Calculus of variations
  • Mathematical analysis
  • MATHEMATICS
  • Path integrals
  • Random variables
  • MATHEMATICS
  • Calculus of variations
  • Mathematical analysis
  • Path integrals
  • Random variables
Label
A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration, Patrick Muldowney
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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{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
Control code
778857698
Dimensions
unknown
Extent
1 online resource
Form of item
online
Isbn
9781118166406
Lccn
2012008712
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
ebc861717
http://library.link/vocab/ext/overdrive/overdriveId
414750
Specific material designation
remote
System control number
(OCoLC)778857698
Label
A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration, Patrick Muldowney
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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{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
Control code
778857698
Dimensions
unknown
Extent
1 online resource
Form of item
online
Isbn
9781118166406
Lccn
2012008712
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
ebc861717
http://library.link/vocab/ext/overdrive/overdriveId
414750
Specific material designation
remote
System control number
(OCoLC)778857698

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