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arxiv: 1704.05582 · v1 · pith:5CLO7FTTnew · submitted 2017-04-19 · 🧮 math.PR

Schauder estimates for stochastic transport-diffusion equations with L\'{e}vy processes

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keywords estimateslderschaudertransport-diffusioncoefficientsconsidercontinuousderive
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We consider a transport-diffusion equation with L\'{e}vy noises and H\"{o}lder continuous coefficients. By using the heat kernel estimates, we derive the Schauder estimates for the mild solutions. Moreover, when the transport term vanishes and $p=2$, we show that the H\"{o}lder index in space variable is optimal.

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