By Yasushi Ishikawa

This monograph is a concise advent to the stochastic calculus of diversifications (also referred to as Malliavin calculus) for techniques with jumps. it's written for researchers and graduate scholars who're attracted to Malliavin calculus for leap procedures. during this booklet "processes with jumps" contains either natural bounce techniques and jump-diffusions. the writer offers many effects in this subject in a self-contained method; this additionally applies to stochastic differential equations (SDEs) "with jumps".

The booklet additionally comprises a few functions of the stochastic calculus for tactics with jumps to the regulate thought and mathematical finance. particularly, asymptotic expansions functionals similar with monetary resources of jump-diffusion are supplied in response to the idea of asymptotic enlargement at the Wiener–Poisson house. fixing the Hamilton–Jacobi–Bellman (HJB) equation of integro-differential variety is said with fixing the classical Merton challenge and the Ramsey theory.

The box of bounce approaches is these days fairly wide-ranging, from the Lévy tactics to SDEs with jumps. contemporary advancements in stochastic research have enabled us to precise quite a few leads to a compact shape. in the past, those themes have been hardly mentioned in a monograph.

**Contents:**Preface

Preface to the second one edition

Introduction

Lévy strategies and Itô calculus

Perturbations and homes of the likelihood law

Analysis of Wiener–Poisson functionals

Applications

Appendix

Bibliography

List of symbols

Index

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