Stochastic calculus of variations for jump processes /
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"...
| Основен автор: | Ishikawa, Yasushi, 1959 October 1- |
|---|---|
| Формат: | Електронна книга |
| Език: | English |
| Публикувано: |
Berlin :
De Gruyter,
[2013]
|
| Серия: |
De Gruyter studies in mathematics.
|
| Предмети: | |
| Онлайн достъп: |
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=604319 |
| Подобни документи: |
Print version::
Stochastic calculus of variations for jump processes. |
Съдържание:
- 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.
- 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.
- 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.