对称Levy噪声下单阱势中的Stationary states
Stationary states in single-well potentials under symmetric Levy noises
摘要：
讨论了对称$α$稳定噪声作用下次谐波势$V(x) \propto |x|^c$，$c<2$的定态存在性.我们分析表明，存在的必要条件的稳定状态是$c>2-α$。这些态的特征在于重尾概率密度函数，对于$|x| \to \infty$，其衰减为$P(x) \propto x^{-(c+α-1)}$，即稳态比相应的$α$稳定律具有更重的尾。蒙特卡罗模拟证实了这种定态的存在和相应概率密度尾部的形式。
英文摘要：
We discuss the existence of stationary states for subharmonic potentials $V(x) \propto |x|^c$, $c<2$, under action of symmetric $α$-stable noises. We show analytically that the necessary condition for the existence of the steady state is $c>2-α$. These states are characterized by heavy-tailed probability density functions which decay as $P(x) \propto x^{-(c+α-1)}$ for $|x| \to \infty$, i.e. stationary states posses a heavier tail than the corresponding $α$-stable law. Monte Carlo simulations confirm the existence of such stationary states and the form of the tails of corresponding probability densities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
