指数a.s.非正则系数一维扩散的同步
Exponential a.s. synchronization of one-dimensional diffusions with non-regular coefficients
摘要：
研究了一类实值扩散方程的渐近性态，该扩散方程的非正则漂移是一个耗散项和一个有界可测项之和。我们证明了两个轨迹的扩散收敛a.s.当耗散系数足够大时，它们之间的相互作用将以指数的显式速率进行。在$L_p$中得到了类似的结果。
英文摘要：
We study the asymptotic behaviour of a real-valued diffusion whose non-regular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge a.s. 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.
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