Asymptotics of damped periodic motions with random initial speed

Yuliy Baryshnikov, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review

Abstract

We consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the probability law of the stopping position of the motion converges to a distribution depending only on the motion equation. Here the time of stopping is either a constant or the first time instant at which the velocity vanishes, and the initial velocity is of the form αU + β, where U is a fixed random variable and α and/or β tend to infinity.

Original languageEnglish
Pages (from-to)5-21
Number of pages17
JournalMathematische Nachrichten
Volume189
DOIs
Publication statusPublished - Jan 1 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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