REVIEW 1 cited by
Rough weak solutions for singular L\'evy SDEs
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Rough weak solutions for singular L\'evy SDEs
read the original 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.
Forward citations
Cited by 1 Pith paper
-
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.