Escape rate of the Brownian motions on hyperbolic spaces
Yuichi Shiozawa
TL;DR
This paper investigates how quickly Brownian motion escapes in hyperbolic spaces, using radial expressions and a generalized Kolmogorov test to determine escape rates.
Contribution
It introduces a method to compute escape rates of Brownian motion on hyperbolic spaces through radial analysis and a generalized Kolmogorov test.
Findings
Escape rate is characterized by radial Brownian motion expressions.
A generalized Kolmogorov test effectively determines escape rates.
Method provides a new way to analyze stochastic processes on hyperbolic spaces.
Abstract
We discuss the escape rate of the Brownian motion on a hyperbolic space. We point out that the escape rate is determined by using the Brownian expression of the radial part and a generalized Kolmogorov's test for the one dimensional Brownian motion.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Markov Chains and Monte Carlo Methods · Diffusion and Search Dynamics