TY - GEN A1 - Milstein, Grigori A1 - Schoenmakers, John A1 - Spokoiny, Vladimir T1 - Forward and reverse representations for Markov chains N2 - In this paper we carry over the concept of reverse probabilistic representa- tions developed in Milstein, Schoenmakers, Spokoiny (2004) for diffusion pro- cesses, to discrete time Markov chains. We outline the construction of reverse chains in several situations and apply this to processes which are connected with jump-diffusion models and finite state Markov chains. By combining forward and reverse representations we then construct transition density esti- mators for chains which have root-N accuracy in any dimension and consider some applications. Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/403 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4034 ER -