Stochastic calculus with respect to Gaussian processes

Authors
Alos, E Mazet, O Nualart, D
Citation
E. Alos et al., Stochastic calculus with respect to Gaussian processes, ANN PROBAB, 29(2), 2001, pp. 766-801
Citations number
22
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798 → ACNP
Volume
29
Issue
2
Year of publication
2001
Pages
766 - 801
Database
ISI
SICI code
0091-1798(200104)29:2<766:SCWRTG>2.0.ZU;2-M
Abstract
In this paper we develop a stochastic calculus with respect to a Gaussian p rocess of the form B-t = integral (t)(0) K(t, s) dW(s), where W is a Wiener process and K(t, s) is a square integrable kernel, using the techniques of the stochastic calculus of variations. We deduce change-of-variable formul as for the indefinite integrals and we study the approximation by Riemann s ums. The particular case of the fractional Brownian motion is discussed.