Energy of taut strings accompanying random walk
Mikhail Lifshits, A. Siuniaev · Probability and Mathematical Statistics · 2020
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.