Approximating a diffusion by a finite-state hidden Markov model

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Kontoyiannis, I.¹  Meyn, S. P.² 

[1] Athens Univ Econ & Business, Dept Informat, Patiss 76, Athens 10434, Greece

[2] Univ Florida, Dept Elect & Comp Engn, Gainesville, FL USA

关键词: Markov process;    Hidden Markov model;    Hypoelliptic diffusion;    Stochastic Lyapunov function;    Discrete spectrum;   

DOI  :  10.1016/j.spa.2016.11.004

来源: Elsevier

【 摘 要 】

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 Lm space. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free