On the Solution of Stochastic Functional Differential Equations via Memory Gap

Flavia Sancier; Salah Mohammed

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arXiv · 1709.00469

On the Solution of Stochastic Functional Differential Equations via Memory Gap

Flavia Sancier·Salah Mohammed

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Abstract

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.

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Flavia Sancier, Salah Mohammed. 2017-09-01. On the Solution of Stochastic Functional Differential Equations via Memory Gap. https://arxiv.org/abs/1709.00469

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