On the theory of relativistic Brownian motion
General Relativity and Quantum Cosmology
2024-05-30 v1 Probability
Abstract
The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener measure as a weak limit of finite-difference approximations. A formula has been proposed for calculating the probability particle transition during relativistic Brownian motion. Calculations were carried out by three different methods with identical results. Along the way, exact and asymptotic formulas for the volume of some parts and sections of an N-1-dimensional unit cube were obtained. They can have independent value.
Keywords
Cite
@article{arxiv.2405.19282,
title = {On the theory of relativistic Brownian motion},
author = {E. A. Kurianovich and A. I. Mikhailov and I. V. Volovich},
journal= {arXiv preprint arXiv:2405.19282},
year = {2024}
}