Anticipating stochastic Volterra equations
type: Item
instance of: scholarly article
title: Anticipating stochastic Volterra equations
zbMATH Open document ID: 0942.60045
DOI: 10.1016/S0304-4149(97)00075-6
author: Elisa Alòs
author: David Nualart
published in: Stochastic Processes and their Applications
publication date: 2000-03-01T00:00:00Z
review text: Stochastic integral equations of the form \[ X_t=x_0+\int _0^tF(t,s,X_s)ds +\sum _{i=1}^k \int _0^t G_i(t,s,X_s)dW^{i}_s, \qquad t\in [0,T],\tag{1} \] are studied where \(W\) is a \(k\)-dimensional Brownian motion, and the coefficients \(F(t,s,x)\) and \(G_i(t,s,x)\) are \(\mathcal F_t\)-measurable. The integrands \(G_i(t,s,X_s)\) are not necessarily \(\mathcal F_s\)-measurable and the stochastic integrals in (1) are interpreted in the Skorokhod sense. Under suitable conditions on smoothness of the diffusion term, existence, uniqueness, time-continuity and semimartingale property of solutions are proved.
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1409151
zbMATH Keywords: stochastic Volterra equations
zbMATH Keywords: anticipating calculus
MaRDI profile type: Publication
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full work available at URL: s0304-4149(97)00075-6
OpenAlex ID: W2032909216
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description: scientific article; zbMATH DE number 1409151