On the Theory of Relativistic Brownian Motion

被引：0

作者：

Kurianovich, E. A. ^{[1
,2
,3
]}

Mikhailov, A. I. ^{[1
,2
,3
]}

Volovich, I. V. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Gubkina 8, Moscow 119991, Russia

[2] Russian Soc Hist & Philosophy Sci, 1-36 Lyalin lane,bd 2, Moscow 105062, Russia

[3] Lomonosov Moscow State Univ, Philosophy Dept, Moscow 119991, Russia

来源：

P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS | 2024年 / 16卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

relativistic Brownian motion; random processes; path integral method; Wiener measure;

D O I：

10.1134/S207004662402002X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：113 / 127

页数：15

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