Approximating a diffusion by a finite-state hidden Markov model

I. Kontoyiannis and S.P. Meyn

Stochastic Processes and their Applications, 2017, vol. 127, issue 8, 2482-2507

Abstract: For a wide class of continuous-time Markov processes evolving on an open, connected subset of Rd, the following are shown to be equivalent: (i)The process satisfies (a slightly weaker version of) the classical Donsker–Varadhan conditions;(ii)The transition semigroup of the process can be approximated by a finite-state hidden Markov model, in a strong sense in terms of an associated operator norm;(iii)The resolvent kernel of the process is ‘v-separable’, that is, it can be approximated arbitrarily well in operator norm by finite-rank kernels. Under any (hence all) of the above conditions, the Markov process is shown to have a purely discrete spectrum on a naturally associated weighted L∞ space.

Keywords: Markov process; Hidden Markov model; Hypoelliptic diffusion; Stochastic Lyapunov function; Discrete spectrum (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spa.2016.11.004

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