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

Mikhail Yu. Romanovsky

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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^†^a, b, c
^aPI "Science and Innovation", Bol'shaya Ordynka str. 24, Moscow, 119017, Russian Federation
^bANO National Center for Physics and Mathematics, Parkovaya Str. 1, build. 3, Sarov, Nizhny Novgorod Region, 607182, Russian Federation
^cRussian National Research Medical University named after N.I. Pirogov, Ostrovitianov str. 1, Moscow, 117997, Russian Federation

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.

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Keywords: delta-function, probability density, microfield distribution
PACS: 02.50.−r, 05.20.−y, 41.20.−q (all)
DOI: 10.3367/UFNe.2024.08.039738
URL: https://ufn.ru/en/articles/2024/10/g/
Citation: Romanovsky M Yu "On R.L. Stratonovich's formula for transition from dynamic to probabilistic measurements and its connection with operations on distribution functions of random variables" Phys. Usp. 67 (10) (2024)

Received: 4th, June 2024, revised: 8th, August 2024, accepted: 10th, August 2024

Оригинал: Романовский М Ю «О формуле Р.Л. Стратоновича перехода от динамических измерений к вероятностным и её связи с операциями над функциями распределения случайных величин» УФН 194 1118–1127 (2024); DOI: 10.3367/UFNr.2024.08.039738