237 research outputs found
On invariant measures of stochastic recursions in a critical case
We consider an autoregressive model on defined by the recurrence
equation , where are i.i.d. random
variables valued in and (critical case). It was proved by Babillot, Bougerol and Elie that
there exists a unique invariant Radon measure of the process . The aim
of the paper is to investigate its behavior at infinity. We describe also
stationary measures of two other stochastic recursions, including one arising
in queuing theory.Comment: Published in at http://dx.doi.org/10.1214/105051607000000140 the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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