Let E,F two Polish spaces and [X_n,Y_n], [X,Y] random variables with values in Etimes F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded function f on Etimes F, the conditional expectation of f(X_n,Y_n) given Y_n converges in distribution to the conditional expectation of f(X,Y) given Y.
I. Crimaldi, L. Pratelli (2005). Convergence results for conditional expectations. BERNOULLI, 11, 737-745 [10.3150/bj/1126126767].
Convergence results for conditional expectations
CRIMALDI, IRENE;
2005
Abstract
Let E,F two Polish spaces and [X_n,Y_n], [X,Y] random variables with values in Etimes F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded function f on Etimes F, the conditional expectation of f(X_n,Y_n) given Y_n converges in distribution to the conditional expectation of f(X,Y) given Y.File in questo prodotto:
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