Pathwise vs. path-by-path uniqueness

2020/01/09 by Shaposhnikov, Alexander, Wresch, Lukas
#34F05 #60G17 #60H10 #60J65 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2001.02869

Abstract

We construct a series of stochastic differential equations of the form dX_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.

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