Forward and reverse representations for Markov chains |
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Authors: | GN Milstein JGM Schoenmakers V Spokoiny |
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Institution: | 1. Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany;2. Ural State University, Ekaterinburg, Russia |
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Abstract: | In this paper we carry over the concept of reverse probabilistic representations developed in Milstein, Schoenmakers, Spokoiny G.N. Milstein, J.G.M. Schoenmakers, V. Spokoiny, Transition density estimation for stochastic differential equations via forward–reverse representations, Bernoulli 10 (2) (2004) 281–312] 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. |
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Keywords: | 60J05 60H10 62G07 65C05 |
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