论文标题
噪音加强的布朗尼动议的通用性
Universality of Noise Reinforced Brownian Motions
论文作者
论文摘要
噪音增强的布朗运动是一个中心的高斯过程$ \ hat b =（\ hat b（t））_ {t \ geq 0} $，带有协方差$ e（\ hat b（t）\ hat b（s）=（s））=（s））=（1-2p） t，$ p \ in（0,1/2）$是增强参数。我们的主要目的是建立Donsker的不变性原则，以在扩散政权中进行大型的步进式随机步行，更具体地说，表明$ \ hat b $是前者的普遍缩放限制。这扩展了关于所谓大象随机行走的渐近行为的已知结果。
A noise reinforced Brownian motion is a centered Gaussian process $\hat B=(\hat B(t))_{t\geq 0}$ with covariance $E(\hat B(t)\hat B(s))=(1-2p)^{-1}t^ps^{1-p} \quad \text{for} \quad 0\leq s \leq t,$ where $p\in(0,1/2)$ is a reinforcement parameter. Our main purpose is to establish a version of Donsker's invariance principle for a large family of step-reinforced random walks in the diffusive regime, and more specifically, to show that $\hat B$ arises as the universal scaling limit of the former. This extends known results on the asymptotic behavior of the so-called elephant random walk.
