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For a countable-state Markov decision process we introduce an embedding which produces a finite-state Markov decision process. The finite-state embedded process has the same optimal cost, and moreover, it has the same dynamics as the original process when restricting to the approximating set. The embedded process can be used as an approximation which, being finite, is more convenient for comput...

In this paper, we consider a continuous-time autoregressive fractionally integrated moving average (CARFIMA) model, which is defined as the stationary solution of a stochastic differential equation driven by a standard fractional Brownian motion. Like the discrete-time ARFIMA model, the CARFIMA model is useful for studying time series with short memory, long memory and antipersistence. We inves...

Let {Yi;-oc < i < c~} be a doubly infinite sequence of identically distributed and (b-mixing random variables, (ai; ~ < i < oc} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence of {Ek=xn ~io~=_¢xz ai+kYi/nt/,; n>~ 1} under some suitable conditions. AMS classification: 60G50; 60F15

We investigate how large deviations events cluster in the framework of an infinite moving average process with light-tailed noise and long memory. The memory makes clusters larger, asymptotic behaviour size turns out to be described by first hitting time a randomly shifted fractional Brownian motion drift.