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Forward and reverse representations for Markov chains

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  • Milstein, G.N.
  • Schoenmakers, J.G.M.
  • Spokoiny, V.

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.

Suggested Citation

  • Milstein, G.N. & Schoenmakers, J.G.M. & Spokoiny, V., 2007. "Forward and reverse representations for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1052-1075, August.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:8:p:1052-1075
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    References listed on IDEAS

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    1. Saavedra, Ángeles & Cao, Ricardo, 1999. "Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 129-155, April.
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