Forward and reverse representations for Markov chains

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1052-1075
Number of pages24
JournalStochastic Processes and their Applications
Issue number8
Publication statusPublished - Aug 2007
Externally publishedYes


  • Estimation of risk
  • Forward and reverse Markov chains
  • Monte Carlo simulation
  • Transition density estimation


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