p-Adic Brownian Motion as a Limit of Discrete Time Random Walks

Autor:	David Weisbart, Erik Makino Bakken
Rok vydání:	2019
Předmět:	Diffusion equation Mathematics::Probability Discrete time and continuous time Differential equation Stochastic process Complex system Statistical and Nonlinear Physics Limit (mathematics) Statistical physics Random walk Mathematical Physics Brownian motion Mathematics
Zdroj:	Communications in Mathematical Physics. 369:371-402
ISSN:	1432-0916 0010-3616
DOI:	10.1007/s00220-019-03447-y
Popis:	The p-adic diffusion equation is a pseudo differential equation that is formally analogous to the real diffusion equation. The fundamental solutions to pseudo differential equations that generalize the p-adic diffusion equation give rise to p-adic Brownian motions. We show that these stochastic processes are similar to real Brownian motion in that they arise as limits of discrete time random walks on grids. While similar to those in the real case, the random walks in the p-adic setting are necessarily non-local. The study of discrete time random walks that converge to Brownian motion provides intuition about Brownian motion that is important in applications and such intuition is now available in a non-Archimedean setting.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c404c6fdd9c5caeaa306260dccb3b493 https://doi.org/10.1007/s00220-019-03447-y Zobrazit plný text záznamu Plný text ve formátu PDF