English

Pathwise vs. path-by-path uniqueness

Probability 2020-12-29 v3

Abstract

We construct a series of stochastic differential equations of the form dXt=b(t,Xt)dt+dBtdX_t = b(t, X_t) dt + dB_t which exhibit nonuniqueness in the path-by-path sense while having a unique adapted solution in the sense of stochastic processes, i.e. pathwise uniqueness holds.

Keywords

Cite

@article{arxiv.2001.02869,
  title  = {Pathwise vs. path-by-path uniqueness},
  author = {Alexander Shaposhnikov and Lukas Wresch},
  journal= {arXiv preprint arXiv:2001.02869},
  year   = {2020}
}