Geodesic
Simultaneaous approximation of a family of (stochastic) differential equations
Philippe Carmona1 ; Laure Coutin1
1Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
ESAIM. Proceedings, Tome 5 (1998), pp. 69-74

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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.
DOI : 10.1051/proc:1998013

Philippe Carmona  1   ; Laure Coutin  1

1 Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France 
Philippe Carmona; Laure Coutin. Simultaneaous approximation of a family of (stochastic) differential equations. ESAIM. Proceedings, Tome 5 (1998), pp. 69-74. doi: 10.1051/proc:1998013
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     title = {Simultaneaous approximation of a family of (stochastic) differential equations},
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     year = {1998},
     volume = {5},
     doi = {10.1051/proc:1998013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:1998013/}
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