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arXiv · 1910.06836

Inverting the Ray-Knight identity on the line

Titus Lupu·Christophe Sabot·Pierre Tarrès
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Abstract

Using a divergent Bass-Burdzy flow we construct a self-repelling one-dimensional diffusion. Heuristically, it can be interpreted as a solution to an SDE with a singular drift involving a derivative of the local time. We show that this self-repelling diffusion inverts the second Ray-Knight identity on the line. The proof goes through an approximation by a self-repelling jump processes that has been previously shown by the authors to invert the Ray-Knight identity in the discrete.

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Titus Lupu, Christophe Sabot, Pierre Tarrès. 2019-10-15. Inverting the Ray-Knight identity on the line. https://doi.org/10.1214/21-ejp657

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