论文标题
具有快速随机切换的系统的固定密度的规律性
Regularity of the stationary density for systems with fast random switching
论文作者
论文摘要
我们考虑通过在紧凑型集合上通过有限的平滑矢量场产生的流中随机切换而获得的分段确定性Markov过程。我们在矢量字段上获得Hörmander-type条件，保证固定密度为：$ c^k $，只要跳跃速度足够快，对于任何$ k <\ \ iffty $；每当跳高速度足够缓慢且半连续的速度较低时，无论跳跃速度如何，无限。我们的证明是概率的，依赖于停止时间的新应用。
We consider the piecewise-deterministic Markov process obtained by randomly switching between the flows generated by a finite set of smooth vector fields on a compact set. We obtain Hörmander-type conditions on the vector fields guaranteeing that the stationary density is: $C^k$ whenever the jump rates are sufficiently fast, for any $k<\infty$; unbounded whenever the jump rates are sufficiently slow and lower semi-continuous regardless of the jump rates. Our proofs are probabilistic, relying on a novel application of stopping times.
