Bernoulli

  • Bernoulli
  • Volume 11, Number 4 (2005), 737-745.

Convergence results for conditional expectations

Irene Crimaldi and Luca Pratelli

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Abstract

Let E,F be two Polish spaces and [Xn,Yn],[X,Y] random variables with values in E×F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded continuous function f on E×F, the conditional expectation of f(Xn,Yn) given Yn converges in distribution to the conditional expectation of f(X,Y) given Y.

Article information

Source
Bernoulli Volume 11, Number 4 (2005), 737-745.

Dates
First available in Project Euclid: 7 September 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1126126767

Digital Object Identifier
doi:10.3150/bj/1126126767

Mathematical Reviews number (MathSciNet)
MR2158258

Zentralblatt MATH identifier
1074.60019

Keywords
conditional expectation Skorohod's theorem weak convergence of probability measures

Citation

Crimaldi, Irene; Pratelli, Luca. Convergence results for conditional expectations. Bernoulli 11 (2005), no. 4, 737--745. doi:10.3150/bj/1126126767. https://projecteuclid.org/euclid.bj/1126126767.


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References

  • [1] Goggin, E.M. (1994) Convergence in distribution of conditional expectations. Ann. Probab., 22(2), 1097-1114.
  • [2] Goggin, E.M. (1997) A L1-approximation for conditional expectations. Stochastics Stochastics Rep., 60, 85-106.