Journal of Theoretical Probability

, Volume 2, Issue 4, pp 461–474

On conditional weak convergence

  • T. J. Sweeting

DOI: 10.1007/BF01051878

Cite this article as:
Sweeting, T.J. J Theor Probab (1989) 2: 461. doi:10.1007/BF01051878


In this paper we discuss a number of technical issues associated with conditional weak convergence. The main modes of convergence of conditional probability distributions areuniform, probability, andalmost sure convergence in the conditioning variable. General results regarding conditional convergence are obtained, including details of sufficient conditions for each mode of convergence, and characterization theorems for uniform conditional convergence.

Key Words

Conditional limit theoremsuniform weak convergenceequicontinuityconvergence of random measures

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • T. J. Sweeting
    • 1
  1. 1.Department of MathematicsUniversity of SurreyGuildfordEngland