This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B

This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution)...

Let (Xn) be a sequence of integrable real random variables, adapted to a filtration (Gn). Define: Cn = n^(1/2) {1/n SUM(k=1:n) Xk - E(Xn+1 | Gn) } and Dn = n^(1/2){ E(Xn+1 | Gn)-Z } where Z is the a.s. limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn,Dn) -- N(0,U) × N(0,V) stably...

This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution)...