soxumis saxelmwifo universitetis S r o m e b i VII

E Tsn 2 c E T1as1 sn n g ˆ1 na231aag c 24The lemma is proved.s2u EF uFu1a2udu O n h gudu1aags2u du.Let us introduce the following random processes:assdu TTnnt Fut n Fˆu EFˆuat Fut n Fˆu Fuannn du.du,Theorem 5.1 0 . Let the conditions of the item (a) of Theorem 4 be fulfilled.Then for all continuous functionals C a, 1a ,f on the distribution f Tntconverges to the distributionf W t awhere Wt a, a t 1 a , is a Wiener processwith a correlation function rs, t min t a,s a,W t a 0 , t a .2 0 . Let the conditions of the item (b) of Theorem 4 be fulfilled.Then for all continuous functionals f on Ca, 1a,the distribution f Tn t converges to the distributionf W t a . Proof. First we will show that the finite-dimensional distributionsof processes T nt converge to the finite-dimensional distribution of a process taW , t a . Let us consider one moment of time t 1. We haveto show that28