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VOL. 53 | 2009 Time evolution with and without remote past
Yoichiro Takahashi

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose


We usually discuss the time evolution from the present to the future or from the past, precisely, from some fixed initial time in the past, to the present or to the future. But we sometimes consider the time evolution from the remote past to the remote future as in the theory of stationary stochastic processes or dynamical systems. In the present paper we consider time evolutions governed by noise driven automorphism on locally compact abelian groups and give a necessary and sufficient condition for the time evolution to admit remote past. It turns out that to admit the remote past is fairly restrictive.


Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1217.37050
MathSciNet: MR2582432

Digital Object Identifier: 10.2969/aspm/05310347

Primary: 60G50
Secondary: 37H10 , 60J05

Keywords: automorphisms of groups , nonstrong solutions , random time evolution , random walks on groups , remote past , stochastic difference equartions

Rights: Copyright © 2009 Mathematical Society of Japan


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