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.

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/
Scopus

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2024PhyU...67.1056R
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 1056–1064 (2024)

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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

References (32) Similar articles (20) ↓

I.M. Arbekov, S.N. Molotkov “Quantum random number generators, extraction of provably random bit sequences from Markov chain trajectories” Phys. Usp. 67 919–937 (2024)
B.M. Bolotovskii, S.N. Stolyarov “Radiation from and energy loss by charged particles in moving media” Sov. Phys. Usp. 35 (2) 143–150 (1992)
V.V. Brazhkin “Why does statistical mechanics 'work' in condensed matter?” Phys. Usp. 64 1049–1057 (2021)
B.M. Bolotovskii, A.V. Serov “Features of the transition radiation field” Phys. Usp. 52 487–493 (2009)
G.N. Gaidukov, A.A. Abramov “An interpretation of the energy conservation law for a point charge moving in a uniform electric field” Phys. Usp. 51 163–166 (2008)
A.A. Golubkov, V.A. Makarov “Boundary conditions for electromagnetic field on the surface of media with weak spatial dispersion” Phys. Usp. 38 325–332 (1995)
I.I. Abbasov, B.M. Bolotovskii, V.A. Davydov “High-frequency asymptotic behavior of radiation spectra of moving charges in classical electrodynamics” Sov. Phys. Usp. 29 788–796 (1986)
O.G. Bakunin “Correlation and percolation properties of turbulent diffusion” Phys. Usp. 46 733–744 (2003)
S.M. Stishov “On the thermodynamics of simple systems” Phys. Usp. 67 912–918 (2024)
N.N. Rosanov, R.M. Arkhipov, M.V. Arkhipov “On laws of conservation in electrodynamics of continuous media (on the occasion of the 100th anniversary of the S.I. Vavilov State Optical Institute)” Phys. Usp. 61 1227–1233 (2018)
I.N. Toptygin, K. Levina “Energy—momentum tensor of the electromagnetic field in dispersive media” Phys. Usp. 59 141–152 (2016)
V.S. Beskin, A.A. Zheltoukhov “On the anomalous torque applied to a rotating magnetized sphere in a vacuum” Phys. Usp. 57 799–806 (2014)
G.N. Bochkov, Yu.E. Kuzovlev “Fluctuation-dissipation relations: achievements and misunderstandings” Phys. Usp. 56 590–602 (2013)
V.B. Morozov “On the question of the electromagnetic momentum of a charged body” Phys. Usp. 54 371–374 (2011)
D.V. Karlovets “On dual representation in classical electrodynamics” Phys. Usp. 53 817–824 (2010)
V.P. Makarov, A.A. Rukhadze “Force acting on a substance in an electromagnetic field” Phys. Usp. 52 937–943 (2009)
A.P. Vinogradov, A.V. Dorofeenko, S. Zouhdi “On the problem of the effective parameters of metamaterials” Phys. Usp. 51 485–492 (2008)
A.M. Dykhne, A.A. Snarskii, M.I. Zhenirovskii “Stability and chaos in randomly inhomogeneous two-dimensional media and LC circuits” Phys. Usp. 47 821–828 (2004)
V.I. Klyatskin, K.V. Koshel’ “Simple example of the development of cluster structure of a passive tracer field in random flows” Phys. Usp. 43 717–723 (2000)
B.M. Bolotovskii, A.V. Serov “On the force line representation of radiation fields” Phys. Usp. 40 1055–1059 (1997)

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