Volume 136, Number 4, November 2021
|Number of page(s)||7|
|Published online||04 March 2022|
Selfsimilar stochastic differential equations
Tel Aviv University Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry Tel Aviv, 69978, Israel
Received: 17 September 2021
Accepted: 19 January 2022
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.
© 2022 The author(s)
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