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Issue ESAIM: Proc.
Volume 5, 1998
Fractional Differential Systems: Models, Methods and Applications
Page(s) 69 - 74
DOI http://dx.doi.org/10.1051/proc:1998013

ESAIM: Proc., 1998, Vol. 5, pp. 69-74
DOI: 10.1051/proc:1998013

Simultaneaous approximation of a family of (stochastic) differential equations

Philippe Carmona and Laure Coutin

Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France


Abstract
To approximate the fractional integral of order a in (0,1), we use an integral representation based on exponential functions introduced in a previous paper, and we present a scheme to approximate the whole family of associated linear differential equations: dy(x,t)/dt=u-xy(x,t), for any x positive real. We show how to extend these results to the stochastic case u=''white noise'', the fractional integration of which is a fractional brownian motion.



© EDP Sciences, ESAIM 1998


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