Conditional expansions and their applications

Abstract

In the present article, we will consider a conditional limit theorem and conditional asymptotic expansions. Our discussion will be based on the Malliavin calculus. First, we treat a problem of lifting limit theorems to their conditional counterparts. Next, we provide asymptotic expansions in a general setting including the so-called small σ-models. In order to give a basis to the asymptotic expansion scheme for perturbed jump systems, we will build an extension to the Watanabe theory in part. Finally, we derive the asymptotic expansions ( double Edgeworth expansions) of conditional expectations.