Necessary optimality conditions of quasi-singular controls for a continuous stochastic Rosser-type control problem

Necessary first- and second-order optimality conditions are obtained for one stochastic optimal control problem described by a stochastic system of first-order nonlinear hyperbolic equations; these conditions are the stochastic analogs of the linearized maximum principle and the optimality conditions of quasi-singular controls, respectively. Such control problems are encountered in the optimization of certain chemical-technological processes under the influence of random effects.