METHODOLOGICAL NOTES

On R L Stratonovich's formula for transition from dynamic to probabilistic measurements and its connection with operations on distribution functions of random variables

M. Yu. Romanovsky<sup>abc

a</sup> PE Science and Innovation, Moscow
^b ANO National Center for Physics and Mathematics, Sarov
^c Pirogov Russian National Research Medical University, Moscow

Abstract: The applications of R L Stratonovich's formula [1] for the exact transition from dynamic measurements to probabilistic or thermodynamic measurements are considered. The connection of this formula with known expressions for operations on probability density functions of random variables is given. The application of the formula to the problem of determining the observed physical parameters—fields, potentials, moments—produced by (stochastically moving) charged particles of different multipolar types is demonstrated.

Keywords: delta-function, probability density, microfield distribution.

PACS: 02.50.-r, 05.20.-y, 41.20.-q

Received: June 4, 2024
Revised: August 8, 2024
Accepted: August 10, 2024

DOI: 10.3367/UFNr.2024.08.039738

 English version: Physics–Uspekhi, 2024, 67:10, 1056–1064

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