Stochastic models arising in inventory, insurance, queueing theory, and other areas are considered. The underlying process is a random walk with two absorbing boundaries, 0 and n. It is proved that the introduction of a multi-level control radically changes the asymptotic behavior (as n→∞) of normalized absorption time and simultaneously stabilizes the system. Some optimization problems are solved as well.
KeywordsAsymptotic Behavior Random Walk Limit Distribution Probability Generate Function Control Implementation
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