Papers by Jeffrey Collamore
We study the forward and backward recursions generated by a stochastic fixed point equation (SFPE... more We study the forward and backward recursions generated by a stochastic fixed point equation (SFPE) of the form V d D A maxfV; DgCB, where .A; B; D/ 2 .0; 1/ R 2 , for both the stationary and explosive cases. In the stationary case (when EOElog A < 0/, we present results concerning the precise tail asymptotics for the random variable V satisfying this SFPE. In the explosive case (when EOElog A > 0/, we establish a central limit theorem for the forward recursion generated by the SFPE, namely the process V n D A n maxfV n1 ; D n g C B n , where f.A n ; B n ; D n / W n 2 Z C g is an i.i.d. sequence of random variables. Next, we consider recursions where the driving sequence of vectors, f.A n ; B n ; D n / W n 2 Z C g, is modulated by a Markov chain in general state space. We demonstrate an asymmetry between the forward and backward recursions and develop techniques for estimating the exceedance probability. In the process, we establish an interesting connection between the regularity properties of fV n g and the recurrence properties of an associated-shifted Markov chain. We illustrate these ideas with several examples.
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Papers by Jeffrey Collamore