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Extreme values, range and weak convergence of integrals of Markov chains

1982; Cambridge University Press; Volume: 19; Issue: 02 Linguagem: Inglês

10.1017/s0021900200022762

1475-6072

Peter J. Brockwell, Sidney I. Resnick, N. Pacheco-Santiago,

Stochastic processes and financial applications

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.