In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space–time white noise and the white-colored noise with spatial covariance given by the Riesz kernel or a bounded integrable function. We show that the spatial average over a ball of radius R...
+ = E X0/Ftc + t 0 t 0 t 0 σE X0/Ftc MsdWs + bE X0/Ftc Msds σE Xs/F[s,t]c dWs + bE Xs/F[s,t]c ds. σE E X0/Fsc Ms/F[s,t]c dWs + bE E X0/Fsc Ms/F[s,t]c ds Ciprian A. Tudor 365 space (Ω , F, P, (Ft)t∈[0,1 ... , 313 - 325 . Ciprian A. Tudor : Laboratoire de Probabilite´s et Mode`les Ale´atoires, Universite´ de Paris 6, 4 Place Jussieu, 75252 Paris Cedex 5, France E- mail address: tudor@ccr . jussieu.fr Volume
+ = E X0/Ftc + t 0 t 0 t 0 σE X0/Ftc MsdWs + bE X0/Ftc Msds σE Xs/F[s,t]c dWs + bE Xs/F[s,t]c ds. σE E X0/Fsc Ms/F[s,t]c dWs + bE E X0/Fsc Ms/F[s,t]c ds Ciprian A. Tudor 365 space (Ω , F, P, (Ft)t∈[0,1 ... , 313 - 325 . Ciprian A. Tudor : Laboratoire de Probabilite´s et Mode`les Ale´atoires, Universite´ de Paris 6, 4 Place Jussieu, 75252 Paris Cedex 5, France E- mail address: tudor@ccr . jussieu.fr Volume
+ = E X0/Ftc + t 0 t 0 t 0 σE X0/Ftc MsdWs + bE X0/Ftc Msds σE Xs/F[s,t]c dWs + bE Xs/F[s,t]c ds. σE E X0/Fsc Ms/F[s,t]c dWs + bE E X0/Fsc Ms/F[s,t]c ds Ciprian A. Tudor 365 space (Ω , F, P, (Ft)t∈[0,1 ... , 313 - 325 . Ciprian A. Tudor : Laboratoire de Probabilite´s et Mode`les Ale´atoires, Universite´ de Paris 6, 4 Place Jussieu, 75252 Paris Cedex 5, France E- mail address: tudor@ccr . jussieu.fr Volume
+ = E X0/Ftc + t 0 t 0 t 0 σE X0/Ftc MsdWs + bE X0/Ftc Msds σE Xs/F[s,t]c dWs + bE Xs/F[s,t]c ds. σE E X0/Fsc Ms/F[s,t]c dWs + bE E X0/Fsc Ms/F[s,t]c ds Ciprian A. Tudor 365 space (Ω , F, P, (Ft)t∈[0,1 ... , 313 - 325 . Ciprian A. Tudor : Laboratoire de Probabilite´s et Mode`les Ale´atoires, Universite´ de Paris 6, 4 Place Jussieu, 75252 Paris Cedex 5, France E- mail address: tudor@ccr . jussieu.fr Volume