Open Access
November 2020 A perturbation analysis of Markov chains models with time-varying parameters
Lionel Truquet
Bernoulli 26(4): 2876-2906 (November 2020). DOI: 10.3150/20-BEJ1210


We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process developed in the literature and that can be used for studying a wide class of Markov processes. To this end, for some families of $V$-geometrically ergodic Markov kernels indexed by a real parameter $u$, we give conditions under which the invariant probability distribution is differentiable with respect to $u$, in the sense of signed measures. Our results also complete the existing literature for the perturbation analysis of Markov chains, in particular when exponential moments are not finite. Our conditions are checked on several original examples of locally stationary processes such as integer-valued autoregressive processes, categorical time series or threshold autoregressive processes.


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Lionel Truquet. "A perturbation analysis of Markov chains models with time-varying parameters." Bernoulli 26 (4) 2876 - 2906, November 2020.


Received: 1 December 2018; Revised: 1 August 2019; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256163
MathSciNet: MR4140532
Digital Object Identifier: 10.3150/20-BEJ1210

Keywords: local stationarity , time-inhomogeneous Markov chains

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 4 • November 2020
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