Geodesic
On the solution of stochastic functional differential equations via memory gap
Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 69-78

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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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     author = {Flavia Sancier and Salah Mohammed},
     title = {On the solution of stochastic functional differential equations via memory gap},
     journal = {Teori\^a slu\v{c}ajnyh processov},
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     publisher = {mathdoc},
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     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a6/}
}
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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/