Stochastic guide for a time-delay object in a positional differential game

A positional differential time-optimal game is considered for a conflict-controlled time-delay object. Minimax and maximin feedback controls are constructed within a scheme that includes an intermediate model object described by an ordinary differential equation and a stochastic guide described by the Ito differential equation. The motion of the guide is based on the real-time solution of a sequence of auxiliary boundary value problems for a parabolic equation with degenerate diffusion term.