On the Ito formula of noncausal type
type: Item
instance of: scholarly article
title: On the Ito formula of noncausal type
zbMATH Open document ID: 0563.60051
author: Shigeyoshi Ogawa
author: Takeshi Sekiguchi
published in: Proceedings of the Japan Academy. Series A
publication date: 1984-01-01T00:00:00Z
review text: Let \(B_ t\) be a real-valued Brownian motion and \(\{\phi_ n\}\) an orthonormal basis in \(L^ 2(0,1)\). Suppose f is a random function satisfying P(\(\int^{1}_{0}f^ 2(t)dt<\infty)=1\) and \(A\subseteq [0,1]\) a measurable set. If \[ \int_{A}fd_{\phi}B:=\lim \sum_{n}\int_{A}f(t,\omega)\phi_ n(t)dt\int^{1}_{0}\phi_ n(t)dB(t) \] converges in probability this expression is called a stochastic integral of noncausal type. The first author [Sur la question d'existence de solutions d'une équation différentielle stochastique du type noncausal. J. Math. Kyoto Univ. 24, 699-704 (1984)] considered stochastic integral equations of noncausal type. In this paper it is shown that the solution satisfies a formula of Ito's type in the non-causal case.
reviewed by: M.Breger
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 3897947
zbMATH Keywords: stochastic integral of noncausal type
zbMATH Keywords: formula of Ito's type
MaRDI profile type: Publication
full work available at URL: pjaa.60.249
OpenAlex ID: W2008781658
cites work: Q4181047
cites work: Sur la question d'existence de solutions d'une équation différentielle stochastique du type noncausal. (On the existence of solutions of a stochastic differential equation of noncausal type)
DOI: 10.3792/PJAA.60.249
description: scientific article; zbMATH DE number 3897947