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.
This work was supported by the French National Research Agency (ANR) grant within the project MALIN (ANR-16-CE93-0003). This work was partly supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). TL acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation. PT acknowledges the support of the National Science Foundation of China (NSFC), grant No. 11771293 and of the Australian Research Council (ARC) grant DP180100613.
"Inverting the Ray-Knight identity on the line." Electron. J. Probab. 26 1 - 25, 2021. https://doi.org/10.1214/21-EJP657