Noncausal Stochastic Calculus | Taschenbuch

Cover: 9784431568254 | Noncausal Stochastic Calculus | Shigeyoshi Ogawa | Taschenbuch | xii

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Beschreibung

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 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.

Zusammenfassung

Is the first book on a stochastic calculus of noncausal nature based on the noncausal stochastic integral introduced by the author in 1979

Begins with the study of fundamental properties of the noncausal stochastic integral by the author

Refers to the relation with other stochastic integrals, causal or not, such as the symmetric integrals and the anticipative integral by A. Skorokhod

Develops the theory along with the study of various noncausal problems in stochastic calculus, most of which are about functional equations

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 210 S. 1 s/w Illustr. 210 p. 1 illus.
ISBN-13:	9784431568254
ISBN-10:	4431568255
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Ogawa, Shigeyoshi
Auflage:	Softcover reprint of the original 1st edition 2017
Hersteller:	Springer Springer Japan KK
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 13 mm
Von/Mit:	Shigeyoshi Ogawa
Erscheinungsdatum:	12.08.2018
Gewicht:	0,347 kg