• Corpus ID: 88522041

A perturbation analysis of some Markov chains models with time-varying parameters

@article{Truquet2017APA,
  title={A perturbation analysis of some Markov chains models with time-varying parameters},
  author={Lionel Truquet},
  journal={arXiv: Statistics Theory},
  year={2017}
}
  • L. Truquet
  • Published 10 June 2017
  • Mathematics
  • arXiv: Statistics Theory
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… 

Poisson Models for Mixtures of Count Time Series

We study nonlinear mixtures of integer-valued ARCH type models for count time series data. We investigate the theoretical properties of these processes and we prove ergodicity and stationarity, under

Two Approaches to the Construction of Perturbation Bounds for Continuous-Time Markov Chains

This paper is largely a review. It considers two main methods used to study stability and to obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with

State-Discretization of V-Geometrically Ergodic Markov Chains and Convergence to the Stationary Distribution

  • Loic Herv'eJ. Ledoux
  • Mathematics, Computer Science
    Methodology and Computing in Applied Probability
  • 2019
TLDR
A discretization scheme providing a computable sequence of probability measures which approximates $\pi$ as $k$ growths to infinity is proposed, and the specific case of first order autoregressive processes with linear and non-linear errors is studied.

References

SHOWING 1-10 OF 34 REFERENCES

Local stationarity and time-inhomogeneous Markov chains

In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in

Measure-Valued Differentiation for Stationary Markov Chains

TLDR
The case of unbounded performance functions and the result on weak differentiability of stationary distributions of Markov chains to unbounded mappings is extended and phantom-type estimators and score function estimators are established.

Perturbation theory for Markov chains via Wasserstein distance

TLDR
This work proves powerful and flexible bounds on the distance of the $n$th step distributions of two Markov chains when one of them satisfies a Wasserstein ergodicity condition, and provides estimates for geometrically ergodic Markov Chains under weak assumptions.

On categorical time series with covariates

We study the problem of stationarity and ergodicity for autoregressive multinomial logistic time series models which possibly include a latent process and are defined by a GARCH-type recursive

Nonparametric regression for locally stationary time series

  • M. Vogt
  • Mathematics, Computer Science
  • 2012
TLDR
A kernel-based method is introduced to estimate the time-varying regression function and asymptotic theory is provided for the estimates and it is shown that the main conditions of the theory are satisfied for a large class of nonlinear autoregressive processes with a time-volatile regression function.

Estimation of the derivative of a stationary measure with respect to a control parameter

The paper deals with a problem which arises in the Monte Carlo optimization of steady state or ergodic systems which can be modelled by Markov chains. The transition probability depends on a

On recursive estimation for time varying autoregressive processes

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the

Parameter stability and semiparametric inference in time-varying ARCH models

In this paper, we develop a complete methodology for detecting time-varying/non time-varying parameters in ARCH processes. For this purpose, we estimate and test various semiparametric versions of

On some nonstationary, nonlinear random processes and their stationary approximations

  • S. Rao
  • Mathematics, Computer Science
  • 2006
TLDR
It is shown that a certain class of nonstationary random processes can locally be approximated by stationary processes and that the derivative processes obtained here have alpha-mixing properties.

Towards a general theory for nonlinear locally stationary processes

In this paper some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as