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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 41, Fasc. 1,
pages 9 - 23
DOI: 10.37190/0208-4147.41.1.2
Published online 25.2.2021
 

Energy of taut strings accompanying random walk

Mikhail A. Lifshits
Anatoly A. Siuniaev

Abstract: We consider the kinetic energy of the taut strings accompanying trajectories of a Wiener process and a random walk. Under certain assumptions on the band width, it is shown that the energy of a taut string accompanying a random walk within a band satisfies the same strong law of large numbers as proved earlier for a Wiener process and a fixed band width. New results for Wiener processes are also obtained.

2010 AMS Mathematics Subject Classification: Primary 60G15; Secondary 60G17, 60F15.

Keywords and phrases: kinetic energy, taut string, Wiener process, random walk, KMT-approximation.

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