Flows generated by stochastic differential equations with reflection

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• Andrey Pilipenko (National Academy of Sciences of Ukraine)
• Friday 09 August 2024, 10:00-11:00
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SSDW02 - Stochastic reflection

It is well known that SDE with smooth coefficients generates a flow of diffeomorphisms of Euclidean space. Consider now a stochastic flow generated by SDE with reflection at the boundary of the domain. It appears that properties of reflective flows are quite different from the properties of flows generated by SDEs in the whole space. We will discuss the following distinctions that arise for any non-trivial reflecting flow:   (a) reflective flows are coalescing;   (b) reflective flows are not continuously differentiable, but have a Sobolev derivative, which satisfies a non-standard stochastic differential equation;   (c) push-forward of an absolute continuous measure under reflective flows contains non-trivial singular component.

This talk is part of the Isaac Newton Institute Seminar Series series.

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