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arXiv · 2001.02869

Pathwise vs. path-by-path uniqueness

Alexander Shaposhnikov·Lukas Wresch
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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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Alexander Shaposhnikov, Lukas Wresch. 2020-01-09. Pathwise vs. path-by-path uniqueness. https://arxiv.org/abs/2001.02869

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