Noncausal Stochastic Calculus (Hardcover, 1st ed. 2017)

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Ito. As is generally known, Ito Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but also its growing possibility as a tool for modeling and analysis in every domain of mathematical sciences. The reader may find there many open problems as well.

General

Imprint:	Springer Verlag,Japan
Country of origin:	Japan
Release date:	August 2017
First published:	2017
Authors:	Shigeyoshi Ogawa
Dimensions:	235 x 155 x 18mm (L x W x T)
Format:	Hardcover
Pages:	210
Edition:	1st ed. 2017
ISBN-13:	978-4-431-56574-1
Categories:	Books > Science & Mathematics > Mathematics > General
LSN:	4-431-56574-4
Barcode:	9784431565741

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