Abstract:
We consider optimal stopping of sequences of random variables satisfying
some asymptotic independence property. Assuming that the embedded planar
point processes converge to a Poisson process, we introduce some further
conditions to obtain approximation of the optimal stopping problem of the
discrete time sequence by the optimal stopping of the limiting Poisson
process. This limiting problem can be solved in several cases. We apply
this method to obtain approximations for the stopping of moving average
sequences, of hidden Markov chains, and of max-autoregressive sequences. We
also briefly discuss extensions to the case of Poisson cluster processes in
the limit.