Stochastic analysis

Itô and malliavin calculus in tandem

Hiroyuki Matsumoto, Setsuo Taniguchi

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

Thanks to the driving forces of the Itô calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.

Original languageEnglish
Title of host publicationStochastic Analysis
Subtitle of host publicationIto and Malliavin Calculus in Tandem
PublisherCambridge University Press
Pages1-346
Number of pages346
ISBN (Electronic)9781316492888
ISBN (Print)9781107140516
DOIs
Publication statusPublished - Jan 1 2016

Fingerprint

Malliavin Calculus
Stochastic Analysis
Calculus
Mathematical Finance
Stochastic Integral Equation
Path Space
Wiener Space
Distribution Theory
Driving Force
Partial differential equation
Physics
Differential equation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Matsumoto, H., & Taniguchi, S. (2016). Stochastic analysis: Itô and malliavin calculus in tandem. In Stochastic Analysis: Ito and Malliavin Calculus in Tandem (pp. 1-346). Cambridge University Press. https://doi.org/10.1017/9781316492888

Stochastic analysis : Itô and malliavin calculus in tandem. / Matsumoto, Hiroyuki; Taniguchi, Setsuo.

Stochastic Analysis: Ito and Malliavin Calculus in Tandem. Cambridge University Press, 2016. p. 1-346.

Research output: Chapter in Book/Report/Conference proceedingChapter

Matsumoto, H & Taniguchi, S 2016, Stochastic analysis: Itô and malliavin calculus in tandem. in Stochastic Analysis: Ito and Malliavin Calculus in Tandem. Cambridge University Press, pp. 1-346. https://doi.org/10.1017/9781316492888
Matsumoto H, Taniguchi S. Stochastic analysis: Itô and malliavin calculus in tandem. In Stochastic Analysis: Ito and Malliavin Calculus in Tandem. Cambridge University Press. 2016. p. 1-346 https://doi.org/10.1017/9781316492888
Matsumoto, Hiroyuki ; Taniguchi, Setsuo. / Stochastic analysis : Itô and malliavin calculus in tandem. Stochastic Analysis: Ito and Malliavin Calculus in Tandem. Cambridge University Press, 2016. pp. 1-346
@inbook{11c3d74371dd4fa4b2136bf82c0c8a66,
title = "Stochastic analysis: It{\^o} and malliavin calculus in tandem",
abstract = "Thanks to the driving forces of the It{\^o} calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.",
author = "Hiroyuki Matsumoto and Setsuo Taniguchi",
year = "2016",
month = "1",
day = "1",
doi = "10.1017/9781316492888",
language = "English",
isbn = "9781107140516",
pages = "1--346",
booktitle = "Stochastic Analysis",
publisher = "Cambridge University Press",
address = "United Kingdom",

}

TY - CHAP

T1 - Stochastic analysis

T2 - Itô and malliavin calculus in tandem

AU - Matsumoto, Hiroyuki

AU - Taniguchi, Setsuo

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Thanks to the driving forces of the Itô calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.

AB - Thanks to the driving forces of the Itô calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.

UR - http://www.scopus.com/inward/record.url?scp=85047290823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047290823&partnerID=8YFLogxK

U2 - 10.1017/9781316492888

DO - 10.1017/9781316492888

M3 - Chapter

SN - 9781107140516

SP - 1

EP - 346

BT - Stochastic Analysis

PB - Cambridge University Press

ER -