Extended versions of Deny's theorem via de Finetti's theorem

Abstract

Recently Lau and Rao [9] and Davies and Shanbhag [3] among others have obtained various extended versions of Deny's theorem on the solution of an integral equation. These results are known to have applications in characterization theory of probability distributions and stochastic processes. We now arrive at these results via de Finetti's theorem on exchangeable random variables and report some of their further applications in characterization problems.