Stochastic differential equations with discontinuous diffusion coefficients

Torres, Soledad; Viitasaari, Lauri

doi:10.1090/tpms/1201

Authors: Soledad Torres and Lauri Viitasaari
Journal: Theor. Probability and Math. Statist. 109 (2023), 159-175
MSC (2020): Primary 60H05; Secondary 60G22, 26A33
DOI: https://doi.org/10.1090/tpms/1201
Published electronically: October 3, 2023
MathSciNet review: 4652998
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Abstract: We study one-dimensional stochastic differential equations of the form $dX_t = \sigma (X_t)dY_t$, where $Y$ is a suitable Hölder continuous driver such as the fractional Brownian motion $B^H$ with $H>\frac 12$. The innovative aspect of the present paper lies in the assumptions on diffusion coefficients $\sigma$ for which we assume very mild conditions. In particular, we allow $\sigma$ to have discontinuities, and as such our results can be applied to study equations with discontinuous diffusions.

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