Theory of Probability and Mathematical Statistics
Stochastic differential equations with discontinuous diffusion coefficients
Soledad Torres and Lauri Viitasaari
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Abstract: We study one-dimensional stochastic differential equations of the form dXt=σ(Xt)dYt, where Y is a suitable Hölder continuous driver such as the fractional Brownian motion BH with H>1/2. The innovative aspect of the present paper lies in the assumptions on diffusion coefficients σ for which we assume very mild conditions. In particular, we allow σ to have discontinuities, and as such our results can be applied to study equations with discontinuous diffusions.
Keywords: Stochastic differential equation, fractional calculus, Hölder continuity, discontinuity, bounded variation
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