On the solution of a general stochastic linear pursuit-evasion game

Abstract

In this paper we have considered the existence and uniqueness of a random solution of a stochastic linear pursuit-evasion game described by a linear stochastic differential equation of the form We give only one transition equation where x( t;ω) can be thought of as the distance between the pursuer and evader, Thus, by a simple transformation, a pursuit-evasion game becomes a contest to bring a point in n-dimenaional space into an e-ball about the origin. The pursuer tries to minimize the time required, while the evader tries to maximize the time. The above transition equation is the most general formalization of a stochastic linear differential equation in the sense that all the functions involved are stochastic. Furthermore, the random function x(t;ω) appears on the right-hand side of the equation. Physically this means that the object(s) being controlled have energy of their own. Integrating the state equation with respect to time l and using some concepts of admissibility theory introduced by Tsokos in...