In this paper we prove, first of all, two inequalities for conditional expectations, from which we easily deduce a result by Landers and Rogge. Then we prove convergence results for conditional expectations of the form P_n[f(X_n)|Y_n] to a conditional expectation of the form P[f(X)|Y]. We study, in particular, the case in which the random variables Y_n, Y are of the type h_n(X_n), h(X).
I. Crimaldi, L. Pratelli (2005). Two inequalities for conditional expectations and convergence results for filters. STATISTICS & PROBABILITY LETTERS, 74, 151-162 [10.1016/j.spl.2005.04.039].
Two inequalities for conditional expectations and convergence results for filters
CRIMALDI, IRENE;
2005
Abstract
In this paper we prove, first of all, two inequalities for conditional expectations, from which we easily deduce a result by Landers and Rogge. Then we prove convergence results for conditional expectations of the form P_n[f(X_n)|Y_n] to a conditional expectation of the form P[f(X)|Y]. We study, in particular, the case in which the random variables Y_n, Y are of the type h_n(X_n), h(X).File in questo prodotto:
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