2 research outputs found
On a class of reflected AR(1) processes
In this paper, we study a reflected AR(1) process, i.e., a process obeying the recursion
= max\{\}, with a sequence of i.i.d. random variables. We find explicit results for the distribution of Zn (in terms of transforms) in case can be written as , with being a sequence of independent random variables which are all
exp() distributed, and i.i.d.; when |a| <1 we can also perform the corresponding
stationary analysis. Extensions are possible to the case that are of phase-type.
Under a heavy-traffic scaling, it is shown that the process converges to a reflected Ornstein-Uhlenbeck process; the corresponding steady-state distribution converges to the distribution of a Normal random variable conditioned on being positive.
Keywords: Reflected processes . queueing . scaling limit