Pathwise vs. path-by-path uniqueness

Abstract

We construct a series of stochastic differential equations of the form $d{X}_t=b(t,X_t)dt+d{B}_t$ 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.

Cited by in corpus (1)

• Path-by-path uniqueness of multidimensional SDE's on the plane with nondecreasing coefficients