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Forward and reverse representations for Markov chains

Author

Listed:
  • Grigori Milstein
  • John Schoenmakers
  • Vladimir Spokoiny

Abstract

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.

Suggested Citation

  • Grigori Milstein & John Schoenmakers & Vladimir Spokoiny, 2006. "Forward and reverse representations for Markov chains," SFB 649 Discussion Papers SFB649DP2006-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2006-041
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    More about this item

    Keywords

    transition density estimation; forward and reverse Markov chains; Monte Carlo simulation; estimation of risk;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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