### 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 language | English |
---|---|

Title of host publication | Stochastic Analysis |

Subtitle of host publication | Ito and Malliavin Calculus in Tandem |

Publisher | Cambridge University Press |

Pages | 1-346 |

Number of pages | 346 |

ISBN (Electronic) | 9781316492888 |

ISBN (Print) | 9781107140516 |

DOIs | |

Publication status | Published - Jan 1 2016 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Stochastic Analysis: Ito and Malliavin Calculus in Tandem.*Cambridge University Press, pp. 1-346. https://doi.org/10.1017/9781316492888

}

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.

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U2 - 10.1017/9781316492888

DO - 10.1017/9781316492888

M3 - Chapter

SN - 9781107140516

SP - 1

EP - 346

BT - Stochastic Analysis

PB - Cambridge University Press

ER -