The 1d self-repelling Brownian polymer, with the singular Dirac interaction, is constructed in the annealed random-environment setting as a unique energy solution, and it is shown to be superdiffusive.
On some path-dependent SDEs involving distributional drifts
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abstract
In this paper, we study (strong and weak) existence and uniqueness of a class of non-Markovian SDEs whose drift contains the derivative in the sense of distributionsof a continuous function.
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Construction of the 1d Self-repelling Brownian Polymer
The 1d self-repelling Brownian polymer, with the singular Dirac interaction, is constructed in the annealed random-environment setting as a unique energy solution, and it is shown to be superdiffusive.