Stochastic Flows and Jump-Diffusions

• Main Author: Kunita, Hiroshi (Author, 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: Probability Theory and Stochastic Modelling, 92
• Subjects: Probabilities.; Economics, Mathematical .; Partial differential equations.; Probability Theory and Stochastic Processes.; Quantitative Finance.; Partial Differential Equations.

This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processe...

Table of Contents:

• Preface
• Introduction
• 1.Probability distributions and stochastic processes
• 2.Stochastic integrals based on Wiener processes and Poisson random measures
• 3.Stochastic differential equations and stochastic flows
• 4.Diffusions, jump-diffusions and heat equations
• 5.Malliavin calculus for Wiener processes and Poisson random measures
• 6.Smooth densities and heat kernels
• 7.Jump-diffusions on manifolds and smooth densities
• Bibliography
• Index.