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The Resource Stochastic analysis in discrete and continuous settings : with normal martingales, Nicolas Privault

Stochastic analysis in discrete and continuous settings : with normal martingales, Nicolas Privault

Label
Stochastic analysis in discrete and continuous settings : with normal martingales
Title
Stochastic analysis in discrete and continuous settings
Title remainder
with normal martingales
Statement of responsibility
Nicolas Privault
Creator
Subject
Language
eng
Summary
"This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance."--Publisher's website
Member of
Cataloging source
BTCTA
http://library.link/vocab/creatorName
Privault, Nicolas
Dewey number
519.22
Illustrations
illustrations
Index
index present
LC call number
QA274.2
LC item number
.P758 2009
Literary form
non fiction
Nature of contents
bibliography
Series statement
Lecture notes in mathematics
Series volume
1982
http://library.link/vocab/subjectName
  • Stochastic analysis
  • Space and time
  • Martingales (Mathematics)
  • Analyse stochastique
  • Espace et temps
  • Martingales (Mathématiques)
  • Stochastische Analysis
Label
Stochastic analysis in discrete and continuous settings : with normal martingales, Nicolas Privault
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 301-307) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
The Discrete Time Case. Normal Martingales ; Stochastic Integrals ; Multiple Stochastic Integrals ; Structure Equations ; Chaos Representation ; Gradient Operator ; Clark Formula and Predictable Representation ; Divergence Operator ; Ornstein-Uhlenbeck Semi-Group and Process ; Covariance Identities ; Deviation Inequalities ; Logarithmic Sobolev Inequalities ; Change of Variable Formula ; Option Hedging ; Notes and References. -- Continuous Time Normal Martingales. Normal Martingales ; Brownian Motion ; Compensated Poisson Martingale ; Compound Poisson Martingale ; Stochastic Integrals ; Predictable Representation Property ; Multiple Stochastic Integrals ; Chaos Representation Property ; Quadratic Variation ; Structure Equations ; Product Formula for Stochastic Integrals ; Itô Formula ; Exponential Vectors ; Vector-Valued Case ; Notes and References. -- Gradient and Divergence Operators. Definition and Closability ; Clark Formula and Predictable Representation ; Divergence and Stochastic Integrals ; Covariance Identities ; Logarithmic Sobolev Inequalities ; Deviation Inequalities ; Markovian Representation ; Notes and References. -- Annihilation and Creation Operators. Duality Relation ; Annihilation Operator ; Creation Operator ; Ornstein-Uhlenbeck Semi-Group ; Deterministic Structure Equations ; Exponential Vectors ; Deviation Inequalities ; Derivation of Fock Kernels ; Notes and References. -- Analysis on the Wiener Space. Multiple Wiener Integrals ; Gradient and Divergence Operators ; Ornstein-Uhlenbeck Semi-Group ; Covariance Identities and Inequalities ; Moment Identities for Skorohod Integrals ; Differential Calculus on Random Morphisms ; Riemannian Brownian Motion ; Time Changes on Brownian Motion ; Notes and References. -- Analysis on the Poisson Space. Poisson Random Measures ; Multiple Poisson Stochastic Integrals ; Chaos Representation Property ; Finite Difference Gradient ; Divergence Operator ; Characterization of Poisson Measures ; Clark Formula and Lévy Processes ; Covariance Identities ; Deviation Inequalities ; Notes and References. -- Local Gradients on the Poisson Space. Intrinsic Gradient on Configuration Spaces ; Damped Gradient on the Half Line ; Damped Gradient on a Compact Interval ; Chaos Expansions ; Covariance Identities and Deviation Inequalities ; Some Geometric Aspects of Poisson Analysis ; Chaos Interpretation of Time Changes ; Notes and References. -- Option Hedging in Continuous Time. Market Model ; Hedging by the Clark Formula ; Black-Scholes PDE ; Asian Options and Deterministic Structure ; Notes and References. -- Appendix. Measurability ; Gaussian Random Variables ; Conditional Expectation ; Martingales in Discrete Time ; Martingales in Continuous Time ; Markov Processes ; Tensor Products of L2 Spaces ; Closability of Linear Operators
Control code
401151192
Dimensions
24 cm
Extent
ix, 310 pages
Isbn
9783642023798
Lccn
2009929703
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)401151192
Label
Stochastic analysis in discrete and continuous settings : with normal martingales, Nicolas Privault
Publication
Bibliography note
Includes bibliographical references (pages 301-307) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
The Discrete Time Case. Normal Martingales ; Stochastic Integrals ; Multiple Stochastic Integrals ; Structure Equations ; Chaos Representation ; Gradient Operator ; Clark Formula and Predictable Representation ; Divergence Operator ; Ornstein-Uhlenbeck Semi-Group and Process ; Covariance Identities ; Deviation Inequalities ; Logarithmic Sobolev Inequalities ; Change of Variable Formula ; Option Hedging ; Notes and References. -- Continuous Time Normal Martingales. Normal Martingales ; Brownian Motion ; Compensated Poisson Martingale ; Compound Poisson Martingale ; Stochastic Integrals ; Predictable Representation Property ; Multiple Stochastic Integrals ; Chaos Representation Property ; Quadratic Variation ; Structure Equations ; Product Formula for Stochastic Integrals ; Itô Formula ; Exponential Vectors ; Vector-Valued Case ; Notes and References. -- Gradient and Divergence Operators. Definition and Closability ; Clark Formula and Predictable Representation ; Divergence and Stochastic Integrals ; Covariance Identities ; Logarithmic Sobolev Inequalities ; Deviation Inequalities ; Markovian Representation ; Notes and References. -- Annihilation and Creation Operators. Duality Relation ; Annihilation Operator ; Creation Operator ; Ornstein-Uhlenbeck Semi-Group ; Deterministic Structure Equations ; Exponential Vectors ; Deviation Inequalities ; Derivation of Fock Kernels ; Notes and References. -- Analysis on the Wiener Space. Multiple Wiener Integrals ; Gradient and Divergence Operators ; Ornstein-Uhlenbeck Semi-Group ; Covariance Identities and Inequalities ; Moment Identities for Skorohod Integrals ; Differential Calculus on Random Morphisms ; Riemannian Brownian Motion ; Time Changes on Brownian Motion ; Notes and References. -- Analysis on the Poisson Space. Poisson Random Measures ; Multiple Poisson Stochastic Integrals ; Chaos Representation Property ; Finite Difference Gradient ; Divergence Operator ; Characterization of Poisson Measures ; Clark Formula and Lévy Processes ; Covariance Identities ; Deviation Inequalities ; Notes and References. -- Local Gradients on the Poisson Space. Intrinsic Gradient on Configuration Spaces ; Damped Gradient on the Half Line ; Damped Gradient on a Compact Interval ; Chaos Expansions ; Covariance Identities and Deviation Inequalities ; Some Geometric Aspects of Poisson Analysis ; Chaos Interpretation of Time Changes ; Notes and References. -- Option Hedging in Continuous Time. Market Model ; Hedging by the Clark Formula ; Black-Scholes PDE ; Asian Options and Deterministic Structure ; Notes and References. -- Appendix. Measurability ; Gaussian Random Variables ; Conditional Expectation ; Martingales in Discrete Time ; Martingales in Continuous Time ; Markov Processes ; Tensor Products of L2 Spaces ; Closability of Linear Operators
Control code
401151192
Dimensions
24 cm
Extent
ix, 310 pages
Isbn
9783642023798
Lccn
2009929703
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)401151192

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