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Inverting the Ray-Knight identity on the line

Lupu, Titus; Sabot, Christophe; Tarrès, Pierre (2021), Inverting the Ray-Knight identity on the line, Electronic Journal of Probability, 26, p. 1-25. 10.1214/21-EJP657

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Electronic Journal of Probability
Volume
26
Publisher
Institute of Mathematical Statistics
Pages
1-25
Publication identifier
Metadata
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Author(s)
Lupu, Titus
Laboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
Sabot, Christophe
Institut Camille Jordan [ICJ]
Tarrès, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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
Subjects / Keywords
isomorphism theorems; Gaussian free field; self-interacting diffusion; local time