Convergence of information, random variables and noise (Q1094306)

Random variables such as state-dependent prices often convey information while entering directly into a decision environment. To understand the convergence properties of behavior based on such random variables, the function mapping any random variable to the information it generates is examined. With respect to convergence in probability of random variables, the information map is continuous with respect to pointwise convergence of information only at completely revealing random variables. Continuity holds when the information map is restricted to any subset of random variables to which the same smooth independent term has been added. Relationships between convergence in distribution of perturbed random variables and convergence in distribution of conditional expectations are also studied.