Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes With Emphasis on the Creation-Annihilation Techniques
A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathema...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2015, 2015
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| Edition: | 1st ed. 2015 |
| Series: | Probability Theory and Stochastic Modelling
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Introduction
- Notations and Basic Analytical Properties
- 1.Reminders on Poisson Random Measures, Lévy Processes and Dirichlet Forms
- 2.Dirichlet Forms and (EID)
- 3.Construction of the Dirichlet Structure on the Upper Space
- 4.The Lent Particle Formula and Related Formulae
- 5.Sobolev Spaces and Distributions on Poisson Space
- 6
- Space-Time Setting and Processes
- 7.Applications to Stochastic Differential Equations driven by a Random Measure
- 8.Affine Processes, Rates Models
- 9.Non Poissonian Cases
- A.Error Structures
- B.The Co-Area Formula
- References