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Normal Approximation for Functions of Hidden Markov Models

Part of: Limit theorems Geometric probability and stochastic geometry Special processes

Published online by Cambridge University Press:  06 June 2022

Christian Houdré  and
George Kerchev
Christian Houdré*
Affiliation:
Georgia Institute of Technology
George Kerchev*
Affiliation:
Université du Luxembourg
*
*Postal address: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160, USA. Email address: houdre@math.gatech.edu
**Postal address: Université du Luxembourg, Unité de Recherche en Mathématiques, Maison du Nombre, 6 Avenue de la Fonte, L-4364 Esch-sur-Alzette, Grand Duché du Luxembourg. Email address: gkerchev@gmail.com
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Abstract

The generalized perturbative approach is an all-purpose variant of Stein’s method used to obtain rates of normal approximation. Originally developed for functions of independent random variables, this method is here extended to functions of the realization of a hidden Markov model. In this dependent setting, rates of convergence are provided in some applications, leading, in each instance, to an extra log-factor vis-à-vis the rate in the independent case.

Keywords

Stein’s methodMarkov chainsgeneralized perturbative approachnormal approximationstochastic geometry

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 60D05: Geometric probability and stochastic geometry
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 2 , June 2022 , pp. 536 - 569
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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