Abstract
Abstract
Diffusion in a logarithmic potential (DLP) attracted significant interest in physics recently. The dynamics of DLP are governed by a Langevin stochastic differential equation (SDE) whose underpinning potential is logarithmic, and that is driven by Brownian motion. The SDE that governs DLP is a particular case of a selfsimilar SDE: one that is driven by a selfsimilar motion, and that produces a selfsimilar motion. This paper establishes the pivotal role of selfsimilar SDEs via two novel universality results. I) Selfsimilar SDEs emerge universally, on the macro level, when applying scaling limits to micro-level SDEs. II) Selfsimilar SDEs emerge universally when applying the Lamperti transformation to stationary SDEs. Using the universality results, this paper further establishes: a novel statistical-analysis approach to selfsimilar Ito diffusions; and the focal importance of DLP.
Subject
General Physics and Astronomy
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. First-passage functionals of Brownian motion in logarithmic potentials and heterogeneous diffusion;Physical Review E;2023-10-31
2. Spectral design of anomalous diffusion;Physica A: Statistical Mechanics and its Applications;2023-09
3. Weird Brownian motion;Journal of Physics A: Mathematical and Theoretical;2023-07-19
4. Entropy of sharp restart;Journal of Physics A: Mathematical and Theoretical;2023-01-13
5. Anomalous diffusion: fractional Brownian motion vs fractional Ito motion;Journal of Physics A: Mathematical and Theoretical;2022-02-23