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A simulation of integral and derivative of the solution of a stochastici integral equation

Nguyen Quy HyNguyen Thi Minh — 1992

Annales Polonici Mathematici

A stochastic integral equation corresponding to a probability space ( Ω , Σ ω , P ω ) is considered. This equation plays the role of a dynamical system in many problems of stochastic control with the control variable u ( · ) : 1 m . One constructs stochastic processes η ( 1 ) ( t ) , η ( 2 ) ( t ) connected with a Markov chain and with the space ( Ω , Σ ω , P ω ) . The expected values of η ( i ) ( t ) (i = 1,2) are respectively the expected value of an integral representation of a solution x(t) of the equation and that of its derivative x u ' ( t ) .

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