Inverting the Ray-Knight identity on the line

Inverting the Ray-Knight identity on the line

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 o...

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Veröffentlicht in:Electronic journal of probability 2021-01, Vol.26 (none), p.1-25
Hauptverfasser: Lupu, Titus, Sabot, Christophe, Tarrès, Pierre
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Mathematics
Probability
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Sabot, Christophe
Tarrès, Pierre
description 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 discrete
doi_str_mv 10.1214/21-EJP657
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subjects Mathematics
Probability
title Inverting the Ray-Knight identity on the line
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