Jump SDEs and the Study of Their Densities A Self-Study Book /

• Main Authors: Kohatsu-Higa, Arturo (Author, http://id.loc.gov/vocabulary/relators/aut), Takeuchi, Atsushi (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Universitext,
• Subjects: Probabilities.; Functional analysis.; Partial differential equations.; Probability Theory and Stochastic Processes.; Functional Analysis.; Partial Differential Equations.

The present book deals with a streamlined presentation of Lévy processes and their densities. It is directed at advanced undergraduates who have already completed a basic probability course. Poisson random variables, exponential random variables, and the introduction of Poisson processes are presen...

Table of Contents:

• Review of some basic concepts of probability theory
• Simple Poisson process and its corresponding SDEs
• Compound Poisson process and its associated stochastic calculus
• Construction of Lévy processes and their corresponding SDEs: The finite variation case
• Construction of Lévy processes and their corresponding SDEs: The infinite variation case
• Multi-dimensional Lévy processes and their densities
• Flows associated with stochastic differential equations with jumps
• Overview
• Techniques to study the density
• Basic ideas for integration by parts formulas
• Sensitivity formulas
• Integration by parts: Norris method
• A non-linear example: The Boltzmann equation
• Further hints for the exercises .