Forward and reverse representations for Markov chains

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

Stochastic Processes and their Applications, 2007, vol. 117, issue 8, 1052-1075

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.

Keywords: Transition; density; estimation; Forward; and; reverse; Markov; chains; Monte; Carlo; simulation; Estimation; of; risk (search for similar items in EconPapers)
Date: 2007
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