Abstract
The value function in the optimal detection problem for jump‐times of a Poisson process satisfies a special system of functional‐differential equations. In this paper, we investigate the system and prove the existence and uniqueness of its solution.
Highlights
AMS subject classifications: 60G99, 60H99. This system appears in the form of a Bellman equation for the value function of the problem of optimal detection of jump-times of a Poisson process investigated by Donchev [2]
This problem is a generalization of the classical Poisson disorder problem (Shiryaev [5], Davis [1], and Wickwire [6]) which is the following
The Poisson disorddr problem is to find a way of using only observations on {zt} to predict the value of 0, and to minimize some cost functional depending on the difference between 0 and its predicted value
Summary
Higher Institute of Food and Flavor Industries Department of Mathematics 4000 Plovdiv, Bulgaria (Received March, 1996; Revised December, 1996). The value function in the optimal detection problem for jump-times of a Poisson process satisfies a special system of functional-differential equations. We investigate the system and prove the existence and uniqueness of its solution.
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