# Approximating a Diffusion by a Hidden Markov Model

Kontoyiannis, I and Meyn, SP Approximating a Diffusion by a Hidden Markov Model. (Unpublished)

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## Abstract

For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, 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 $L_\infty$ space.

Item Type: Article math.PR math.PR UNSPECIFIED Div F > Signal Processing and Communications Cron Job 08 Jan 2018 20:12 18 Aug 2020 12:42