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Approximating a diffusion by a finite-state hidden Markov model

Kontoyiannis, I and Meyn, SP (2017) Approximating a diffusion by a finite-state hidden Markov model. Stochastic Processes and their Applications, 127. pp. 2482-2507. ISSN 0304-4149

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Abstract

© 2016 Elsevier B.V. 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.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:12
Last Modified: 16 Aug 2018 01:59
DOI: