Geodesic
On the solution of stochastic functional differential equations via memory gap
Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 69-78 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present an alternative proof for the existence of solutions of stochastic functional differential equations satisfying a global Lipschitz condition. The proof is based on an approximation scheme in which the continuous path dependence does not go up to the present: there is a memory gap. Strong convergence is obtained by closing the gap. Such approximation is particularly useful when extending stochastic models with discrete delay to models with continuous full finite memory.
Keywords: Stochastic functional differential equations, approximation scheme, memory, delay.
Mots-clés : existence of solutions 
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Flavia Sancier; Salah Mohammed. On the solution of stochastic functional differential equations via memory gap. Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 69-78. http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a6/

[1] T. A. Ahmed, Stochastic Functional Differential Equations with Discontinuous Initial Data, M.Sc. thesis, university of Khartoum, Sudan, 1983

[2] D. R. Bell, S. E. A. Mohammed, “On the solution of stochastic ordinary differential equations via small delays”, Stochastics, 28:4 (1989), 293–299 | MR | Zbl

[3] Y. Hu, S.-E. Mohammed, F. Yan, Discrete-time approximations of stochastic differential systems with memory, Dept. Mathematics, Southern Illinois Univ., Carbondale, 2004 | MR

[4] P. E. Kloeden, E. Platen, H. Shurz, Numerical solution of SDE through computer experiments, v. 1, Springer-Verlag, Berlin-Heidelberg-New York, 1994 | MR | Zbl

[5] H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990 | MR | Zbl

[6] S.-E. A. Mohammed, Stochastic Functional Differential Equations, Pitman 99, Boston-London-Melbourne, 1984 | MR | Zbl

[7] M-K. von Renesse, M. Scheutzow, “Existence and Uniqueness of Solutions of Stochastic Functional Differential Equations”, Random Operators Stochastic Equations, 18:3 (2010), 267–284 | MR | Zbl