Volume 5, 1998Fractional Differential Systems: Models, Methods and Applications
|Page(s)||69 - 74|
|Published online||15 August 2002|
Simultaneaous approximation of a family of (stochastic) differential equations
Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
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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