Jump SDEs and the Study of Their Densities - A Self-Study Book (Paperback, 1st ed. 2019)

The present book deals with a streamlined presentation of Levy 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 presented first, followed by the introduction of Poisson random measures in a simple case. With these tools the reader proceeds gradually to compound Poisson processes, finite variation Levy processes and finally one-dimensional stable cases. This step-by-step progression guides the reader into the construction and study of the properties of general Levy processes with no Brownian component. In particular, in each case the corresponding Poisson random measure, the corresponding stochastic integral, and the corresponding stochastic differential equations (SDEs) are provided. The second part of the book introduces the tools of the integration by parts formula for jump processes in basic settings and first gradually provides the integration by parts formula in finite-dimensional spaces and gives a formula in infinite dimensions. These are then applied to stochastic differential equations in order to determine the existence and some properties of their densities. As examples, instances of the calculations of the Greeks in financial models with jumps are shown. The final chapter is devoted to the Boltzmann equation.

General

Imprint:	Springer Verlag, Singapore
Country of origin:	Singapore
Series:	Universitext
Release date:	August 2019
First published:	2019
Authors:	Arturo Kohatsu-Higa • Atsushi Takeuchi
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	355
Edition:	1st ed. 2019
ISBN-13:	978-981-3297-40-1
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
LSN:	981-3297-40-9
Barcode:	9789813297401

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