This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Milstein, Grigori N.Schoenmakers, John G.M.Spokoiny, Vladimir2016-12-032019-06-2820060946-8633https://doi.org/10.34657/2387https://oa.tib.eu/renate/handle/123456789/3228In this paper we carry over the concept of reverse probabilistic representations developed in Milstein, Schoenmakers, Spokoiny (2004) for diffusion processes, 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 estimators for chains which have root-N accuracy in any dimension and consider some applications.application/pdfeng510Transition density estimationforward and reverse Markov chainsMonte Carlo simulationestimation of riskReport