Time-inhomogeneous markov chains pdf

Continuoustime markov chains 5 the proof is similar to that of theorem 2 and therefore is omitted. The nonhomogeneous case is generally called time inhomogeneous or. Stroocks markov processes book is, as far as i know, the most readily accessible treatment of inhomogeneous markov processes. Ergodicity for time inhomogeneous finite markov chains in general is discussed in 17, 21, 25 where further references can be. Wienerhopf factorization for timeinhomogeneous markov. To get a better understanding of what a markov chain is, and further, how it can be used to sample form a distribution, this post introduces and applies a few basic concepts. Time inhomogeneous markov jump process concepts duration.

A timeinhomogeneous markov process xt with state space s can be identified with the time. In the spirit of some locally stationary processes introduced in the literature, we consider triangular arrays of timeinhomogeneous markov chains, defined by. In this paper, we consider inhomogeneous markov chain models for. Merging and stability for time inhomogeneous finite markov. This is an electronic reprint of the original article published by the institute of mathematical statistics in the annals of applied probability, 2010, vol. The two main notions for our purpose are merging and stability. Theorem 4 provides a recursive description of a continuoustime markov chain.

Abstract in this paper, we study a notion of local stationarity for discrete time markov chains which is useful for applications in statistics. Nonhomogeneous markov chains and their applications. Naturally one refers to a sequence 1k 1k 2k 3 k l or its graph as a path, and each path represents a realization of the markov chain. Local stationarity and timeinhomogeneous markov chains article pdf available in the annals of statistics 474 october 2016 with 46 reads how we measure reads. Wienerhopf factorization for timeinhomogeneous markov chains 3 where. Timeinhomogeneous models arise naturally in settings where one wishes to explicitly model \timeofday e ects or \seasonality e ects or economic growth over time as exogenous variables.

For this reason one refers to such markov chains as time homogeneous or. Pdf local stationarity and timeinhomogeneous markov chains. Therefore by definition we know that the chain is irreducible. More on markov chains, examples and applications section 1. We discuss problems posed by the quantitative study of time inhomogeneous markov chains.

Local stationarity and timeinhomogeneous markov chains lionel truquet. Local stationarity and timeinhomogeneous markov chains 3 and zu niga 41 for nite state spaces. Convergence of some time inhomogeneous markov chains via. Convergence of some time inhomogeneous markov chains via spectral techniques jessica zuniga with laurent salo. Under mcmc, the markov chain is used to sample from some target distribution.

On estimation of expectation of simultaneous renewal time of. Local stationarity and timeinhomogeneous markov chains. Ergodicity concepts for timeinhomogeneous markov chains. In the spirit of some locally stationary processes introducedin the literature. Markov chains are an essential component of markov chain monte carlo mcmc techniques. Discrete time markov chains with r the r journal r project. Im trying to find out what is known about timeinhomogeneous ergodic markov chains where the transition matrix can vary over time. All textbooks and lecture notes i could find initially introduce markov chains this way but then quickly restrict themselves to the timehomogeneous case where you have one transition matrix. Time markov chains dtmcs, filling the gap with what is currently available in. Time inhomogeneous markov chains, wave like behavior, singular values.