MARC Record from harvard_bibliographic_metadata

LEADER: 04595cam a22003373 4500
001 012058191-4
005 20091020174521.0
008 090613s2009 gw a b 001 0 eng d
020 $a9783642023798
020 $a3642023797
035 0 $aocn401151192
040 $aBTCTA$cBTCTA$dKUK
050 00 $aQA274.2$b.P75 2009
090 $aQA274.2$b.P758 2009
100 1 $aPrivault, Nicolas.
245 10 $aStochastic analysis in discrete and continuous settings :$bwith normal martingales /$cNicolas Privault
260 $aBerlin :$bSpringer,$cc2009.
300 $aix, 310 p. :$bill. ;$c24 cm.
490 1 $aLecture notes in mathematics ;$v1982
504 $aIncludes bibliographical references (p. 301-307) and index.
520 $a"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.
505 0 $aThe 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. --
505 0 $aGradient 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. --
505 0 $aAnalysis 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. --
505 0 $aAppendix. 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.
650 0 $aStochastic analysis.
650 0 $aSpace and time.
650 0 $aMartingales (Mathematics)
830 0 $aLecture notes in mathematics (Springer-Verlag) ;$v1982.
988 $a20090817
906 $0OCLC