Noncausal Stochastic Calculus. 1st ed. 2017

種類:

電子ブック

責任表示:

by Shigeyoshi Ogawa

出版情報:

Tokyo : Springer Japan : Imprint: Springer, 2017

著者名:

• Ogawa, Shigeyoshi.
• SpringerLink (Online service)

ISBN:

9784431565765 [4431565760]    

注記:

1 Introduction – Why the Causality? -- 2 Preliminary – Causal calculus -- 3 Noncausal Calculus -- 4 Noncausal Integral and Wiener Chaos -- 5 Noncausal SDEs -- 6 Brownian Particle Equation -- 7 Noncausal SIE -- 8 Stochastic Fourier Transformation -- 9 Appendices to Chapter 2 -- 10 Appendices 2 – Comments and Proofs -- Index.
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 Itô. As is generally known, Itô 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 al

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