The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory

Esa Nummelin and Pekka Tuominen

Stochastic Processes and their Applications, 1983, vol. 15, issue 3, 295-311

Abstract: We derive sufficient conditions for [is proportional to] [lambda] (dx)||Pn(x, ·) - [pi]|| to be of order o([psi](n)-1), where Pn (x, A) are the transition probabilities of an aperiodic Harris recurrent Markov chain, [pi] is the invariant probability measure, [lambda] an initial distribution and [psi] belongs to a suitable class of non-decreasing sequences. The basic condition involved is the ergodicity of order [psi], which in a countable state space is equivalent to [Sigma] [psi](n)Pi{[tau]i[greater-or-equal, slanted]n} 0 and [is proportional to] [psi](t)(1- F(t))dt

Keywords: Markov; chain; non-singular; renewal; processes; rate; of; convergence; splitting (search for similar items in EconPapers)
Date: 1983
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Citations: View citations in EconPapers (8)

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