Department of Mathematics

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    Stochastic Functional Differential Equations with Discontinuous Initial Data
    (University of Khartoum, 1983) Tag El Sir Mohammed Ali Ahmed ; Salah Ahmed Mohammed ; Salah Abd Alla Elsanissi ; Mathematics
    In chapter I we shall layout our notation; state all standing assumptions and some of the theorems and results which we have used throughout the whole work. In chapter I we shall discuss the definition and the existence of Ito integral and masher belated integral and some of their properties. In the first part of chapter two we find sufficient conditions for the existence of a unique solution of a stochastic functional differential equation with discontinuous initial data. The work in the first part of chapter IT is carried out by suitable modifications the work of Mohammed [7]. In the second part of chapter 11, we weaken the conditions on the coefficients of the S.F.D.E (stochastic functional differential equation) and still obtain a unique solution. The work in the second part of chapter 11 is carried out by suitable modifications of the work of Freedman [4] of [4], chapter 5 theorem (2.1) and 2.2». In chapter III we prove an approximation lemma and an approximation theorem which gives us a method for approximating the solution of the S. F. D. E's discussed in chapter 11. The work in chapter III constitutes an extension of the work of Mc Shane (c f [6]; lemma v (3A) and theorem v (4.3)) O