Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 2, Pages 179-192
doi:10.1155/S1048953398000136
A system of functional-differential equations associated with the optimal detection problem for jump-times of a Poisson process
Higher Institute of Food and Flavor Industries, Department of Mathematics, Plovdiv 4000, Bulgaria
Received 1 March 1996; Revised 1 December 1996
Copyright © 1998 Doncho S. Donchev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.