Stochastic Differential Equations with Discontinuous Diffusions

Soledad Torres; Lauri Viitasaari

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arXiv · 1908.03183

Stochastic Differential Equations with Discontinuous Diffusions

Soledad Torres·Lauri Viitasaari

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Abstract

We study one-dimensional stochastic differential equations of form $dX_t = \sigma(X_t)dY_t$, where $Y$ is a suitable H\"older continuous driver such as the fractional Brownian motion $B^H$ with $H>\frac12$. 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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BibTeX RIS

Soledad Torres, Lauri Viitasaari. 2019-08-08. Stochastic Differential Equations with Discontinuous Diffusions. https://arxiv.org/abs/1908.03183

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