A representation for the derivative with respect to the initial data of the solution of an SDE with a non-regular drift and a Gaussian noise

Olga Aryasova; Andrey Pilipenko

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arXiv · 1605.06911

A representation for the derivative with respect to the initial data of the solution of an SDE with a non-regular drift and a Gaussian noise

Olga Aryasova·Andrey Pilipenko

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Abstract

We consider a multidimensional SDE with a Gaussian noise and a drift vector being a vector function of bounded variation. We prove the existence of generalized derivative of the solution with respect to the initial conditions and represent the derivative as a solution of a linear SDE with coefficients depending on the initial process. The representation obtained is a natural generalization of the expression for the derivative in the smooth case. The theory of continuous additive functionals is used.

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Olga Aryasova, Andrey Pilipenko. 2016-06-10. A representation for the derivative with respect to the initial data of the solution of an SDE with a non-regular drift and a Gaussian noise. https://arxiv.org/abs/1605.06911

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