Extreme values, range and weak convergence of integrals of Markov chains
- 1 June 1982
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 19 (2), 272-288
- https://doi.org/10.2307/3213480
Abstract
A study is made of the maximum, minimum and range on [0, t] of the integral process where S is a finite state-space Markov chain. Approximate results are derived by establishing weak convergence of a sequence of such processes to a Wiener process. For a particular family of two-state stationary Markov chains we show that the corresponding centered integral processes exhibit the Hurst phenomenon to a remarkable degree in their pre-asymptotic behaviour.Keywords
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