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

Doncho S. Donchev

 Higher Institute of Food and Flavor Industries, Department of Mathematics, Plovdiv 4000, Bulgaria
Received 1 March 1996; Revised 1 December 1996

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.