Abstract. In this work, we are concerned with the Cauchy problem of a delay stochastic differential equation of arbitrary (fractional) orders. The existence (local) of a unique mean square continuous solution is proved. The continuous dependence of the solution on the initial random variable is studied.Mathematics subject classification (2010): 26A33, 34K50.
In this paper, we are concerned with an open-loop Nash differential game. The necessary conditions for an open-loop Nash equilibrium solution are obtained, also the existence for the solution of the dynamical system of the differential game is studied. Picard method is used to find an approximate solution, and the uniform convergence is proved. Finally, we constructed figures for the analysis of the differential game. These results can be applied between economic and financial firms as well as industrial firms.
In this paper, we are concerned with an open-loop Nash differential game. We found the necessary conditions for an open loop Nash equilibrium solution and studied the existence for the solution of the dynamical system of the differential game. Also, we used Picard method to find an approximate solution and the uniform convergence is proved. Finally, we constructed figures for the analysis of the differential game. The results can be applied between economic and financial firms as well as industrial firms.Subject classification: 91A05, 91A10, 91A23, 34A12 and 65L03
<abstract><p>In this paper, we are concerned with a min-max differential game with Cauchy initial value problem (CIVP) as the state trajectory for the differential game, we studied the analytical solution and the approximate solution by using Picard method (PM) of this problem. We obtained the equivalent integral equation to the CIVP. Also, we suggested a method for solving this problem. The existence, uniqueness of the solution and the uniform convergence are discussed for the two methods.</p></abstract>
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