The homing problem for autoregressive processes

Abstract

The problem of maximizing or minimizing the time spent by a stochastic process in an interval is considered for autoregressive processes. The control applied to the system is equal to 0, $b$ or $-b$. Particular cases are considered, and the appropriate integral equations are solved explicitly, either exactly or approximately.

A boundary value problem for a non-linear difference equation

“…The above problem is a particular homing problem; see Whittle [9, p. 289] and [10]. The author has published numerous papers on homing problems; see, for instance, [3] and [4]. Other papers on this topic are the ones by Kuhn [2], Makasu [6] and Kounta and Dawson [1].…”

A Discrete-Time Homing Problem with Two Optimizers

“…The author has written numerous papers on homing problems. In [10,11], these problems where extended to the case of discrete-time Markov chains, whereas in [12] the case of autoregressive processes was treated; see also [13].…”