Stochastic calculus of variations for jump processes /

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This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book processes "with jumps"...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ishikawa, Yasushi, 1959 October 1-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin : De Gruyter, [2013]
Colección:De Gruyter studies in mathematics.
Temas:
Malliavin calculus.
Calculus of variations.
Jump processes.
Calcul de Malliavin.
Calcul des variations.
Processus de sauts.
MATHEMATICS > Probability & Statistics > General.
Calculus of variations
Jump processes
Malliavin calculus
Acceso en línea:Texto completo

MARC

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100 1 |a Ishikawa, Yasushi,  |d 1959 October 1-  |1 https://id.oclc.org/worldcat/entity/E39PCjKjWXmMY7QbVMM8TTCmV3 
245 1 0 |a Stochastic calculus of variations for jump processes /  |c Yasushi Ishikawa. 
260 |a Berlin :  |b De Gruyter,  |c [2013] 
300 |a 1 online resource (viii, 266 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 1 |a De Gruyter Studies in Mathematics 
588 0 |a Print version record. 
504 |a Includes bibliographical references (pages 253-261) and index. 
520 |a This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book processes "with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the c. 
505 0 |a Preface; 0 Introduction; 1 L y processes and It calculus; 1.1 Poisson random measure and L y processes; 1.1.1 L y processes; 1.1.2 Examples of L y processes; 1.1.3 Stochastic integral for a finite variation process; 1.2 Basic materials to SDEs with jumps; 1.2.1 Martingales and semimartingales; 1.2.2 Stochastic integral with respect to semimartingales; 1.2.3 Dolens' exponential and Girsanov transformation; 1.3 It processes with jumps; 2 Perturbations and properties of the probability law; 2.1 Integration-by-parts on Poisson space; 2.1.1 Bismut's method; 2.1.2 Picard's method. 
505 8 |a 3.3.3 The Wiener-Poisson space3.4 Relation with the Malliavin operator; 3.5 Composition on the Wiener-Poisson space (I) -- general theory; 3.5.1 Composition with an element in S'; 3.5.2 Sufficient condition for the composition; 3.6 Smoothness of the density for It processes; 3.6.1 Preliminaries; 3.6.2 Big perturbations; 3.6.3 Concatenation (I); 3.6.4 Concatenation (II) -- the case that (D) may fail; 3.7 Composition on the Wiener-Poisson space (II) -- It processes; 4 Applications; 4.1 Asymptotic expansion of the SDE; 4.1.1 Analysis on the stochastic model. 
505 8 |a 4.1.2 Asymptotic expansion of the density4.1.3 Examples of asymptotic expansions; 4.2 Optimal consumption problem; 4.2.1 Setting of the optimal consumption; 4.2.2 Viscosity solutions; 4.2.3 Regularity of solutions; 4.2.4 Optimal consumption; 4.2.5 Historical sketch; Appendix; Bibliography; List of symbols; Index. 
546 |a English. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Malliavin calculus. 
650 0 |a Calculus of variations. 
650 0 |a Jump processes. 
650 6 |a Calcul de Malliavin. 
650 6 |a Calcul des variations. 
650 6 |a Processus de sauts. 
650 7 |a MATHEMATICS  |x Probability & Statistics  |x General.  |2 bisacsh 
650 7 |a Calculus of variations  |2 fast 
650 7 |a Jump processes  |2 fast 
650 7 |a Malliavin calculus  |2 fast 
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776 0 8 |i Print version:  |a Ishikawa, Yasushi, 1959 October 1-  |t Stochastic calculus of variations for jump processes.  |d Berlin : De Gruyter, [2013]  |z 3110281805  |w (DLC) 2013009951  |w (OCoLC)842307315 
830 0 |a De Gruyter studies in mathematics. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1113344  |z Texto completo 
880 8 |6 505-00/(S  |a 2.1.3 Some previous methods2.2 Methods of finding the asymptotic bounds (I); 2.2.1 Markov chain approximation; 2.2.2 Proof of Theorem 2.3; 2.2.3 Proof of lemmas; 2.3 Methods of finding the asymptotic bounds (II); 2.3.1 Polygonal geometry; 2.3.2 Proof of Theorem 2.4; 2.3.3 Example of Theorem 2.4 -- easy cases; 2.4 Summary of short time asymptotic bounds; 2.4.1 Case that μ(dz) is absolutely continuous with respect to the m-dimensional Lebesgue measure dz; 2.4.2 Case that μ(dz) is singular with respect to dz; 2.5 Auxiliary topics; 2.5.1 Marcus'canonical processes. 
880 8 |6 505-00/(S  |a 2.5.2 Absolute continuity of the infinitely divisible laws2.5.3 Chain movement approximation; 2.5.4 Support theorem for canonical processes; 3 Analysis of Wiener-Poisson functionals; 3.1 Calculus of functionals on the Wiener space; 3.1.1 Definition of the Malliavin-Shigekawa derivative Dt; 3.1.2 Adjoint operator δ = D*; 3.2 Calculus of functionals on the Poisson space; 3.2.1 One-dimensional case; 3.2.2 Multidimensional case; 3.2.3 Characterisation of the Poisson space; 3.3 Sobolev space for functionals over the Wiener-Poisson space; 3.3.1 The Wiener space; 3.3.2 The Poisson Space. 
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