WIAS Preprint No. 1125, (2006)

Forward and reverse representations for Markov chains


  • Milstein, Grigori N.
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 60J05 60H10 62G07 65C05


  • estimation of risk, transition density estimation, forward and reverse Markov chains, Monte Carlo simulation




In 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.

Appeared in

  • Stochastic Process. Appl., 117 (2007) pp. 1052--1075.

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