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.
Rough weak solutions for singular L\'evy SDEs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We introduce a weak solution concept (called "rough weak solutions") for singular SDEs with additive alpha-stable L\'evy noise (including the Brownian noise case) and prove its equivalence to martingale solutions from Kremp, Perkowski '22 in the Young and rough regularity regime. In the rough regime this leads to the construction of certain rough stochastic sewing integrals involved. For rough weak solutions, we can then prove a generalized It\^o formula. Furthermore, we show that canonical weak solutions are wellposed in the Young case (and equivalent to rough weak solutions), while ill-posed in the rough case. For the latter, we construct a counterexample for uniqueness in law.
fields
math.PR 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
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.