Stochastic calculus of variations for jump processes:
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Bibliographic Details
Main Author: Ishikawa, Yasushi 1959 October 1- (Author)
Format: Electronic eBook
Language:English
Published: Berlin De Gruyter [2013]
Series:De Gruyter studies in mathematics
Subjects:
Online Access:FAW01
FAW02
Item Description:Includes bibliographical references (pages 253-261) and index
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
Preface; 0 Introduction; 1 L‌vy processes and It{OCLCbr#99} calculus; 1.1 Poisson random measure and L‌vy processes; 1.1.1 L‌vy processes; 1.1.2 Examples of L‌vy 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 Dol‌ans' exponential and Girsanov transformation; 1.3 It{OCLCbr#99} 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
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{OCLCbr#99} 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{OCLCbr#99} processes; 4 Applications; 4.1 Asymptotic expansion of the SDE; 4.1.1 Analysis on the stochastic model
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
Physical Description:viii, 266 pages
ISBN:9783110282009
3110282003
9781299721739
1299721737
9783110282016
3110282011
9783110281804
3110281805

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