Abstract

We study the asymptotic behavior of a real-valued diffusion whose nonregular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge almost sure to one another at an exponential explicit rate as soon as the dissipative coefficient is large enough. A similar result in L_p is obtained.

中文翻译：

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具有非正则系数的一维扩散的指数几乎确定同步

摘要

我们研究了实值扩散的渐近行为，其非正则漂移是作为耗散项和有界可测量项的总和给出的。我们证明，一旦耗散系数足够大，该扩散的两条轨迹几乎肯定会以指数显式速率相互收敛。在L _p 中获得了类似的结果。