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/
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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)

Stratonovich R L Nonlinear Nonequilibrium Thermodynamics I. Linear And Nonlinear Fluctuation-Dissipation Theorems (Berlin: Springer-Verlag, 1992); Translated from Russian, Stratonovich R L Nelineinaya Neravnovesnaya Termodinamika (Moscow: Nauka, 1985)
Gurbatov S N, Rudenko O V, Saichev A I Waves And Structures In Nonlinear Nondispersive Media: General Theory And Applications To Nonlinear Acoustics (Berlin: Springer-Verlag, 2011); Translated from Russian, Gurbatov S N, Rudenko O V, Saichev A I Volny I Struktury V Nelineinykh Sredakh Bez Dispersii: Prilozheniya K Nelineinoi Akustike (Moscow: Fizmatlit, 2008)
Markov A A Ischislenie Veroyatnostei (Probability Calculus, (K 200-letnemu Yubileyu Zakona Bol’shikh Chisel (To 200-year Anniversary of the Law of Large Numbers))) 3rd ed., rev. and consid. enlarg. (St. Petersburg: Tipografiya Imperatorskoi Akademii Nauk, 1913)
Chandrasekhar S Rev. Mod. Phys. 15 1 (1943); Translated into Russian, Chandrasekhar S Stokhasticheskie Problemy V Fizike I Astronomii (Stochastic Problems In Physics And Astronomy) (Moscow: Gos. Izd. Inostr. Lit., 1947)
Gnedenko B V The Theory Of Probability (Moscow: Mir Publ., 1978); Translated from Russian, Gnedenko B V Kurs Teorii Veroyatnostei (Course In Probability Theory) (Moscow: Nauka, 1988)
Emel’yanov G V, Skitovich V P Zadachnik Po Teorii Veroyatnostei I Matematicheskoi Statistike (Problems On Probability Theory And Mathematical Statistics) (St. Petersburg: Lan’, 2021)
Feller W An Introduction To Probability Theory And Its Applications Vol. 1 (New York: John Wiley and Sons, 1970); Translated into Russian, Feller W Vvedenie V Teoriyu Veroyatnostei I Ee Prilozheniya Vol. 1 (Moscow: Mir, 1984)
Feller W An Introduction To Probability Theory And Its Applications Vol. 2 (New York: John Wiley and Sons, 1971); Translated into Russian, Feller W Vvedenie V Teoriyu Veroyatnostei I Ee Prilozheniya Vol. 2 (Moscow: Mir, 1984)
Holtsmark J Ann. Physik 58 577 (1919)
Fortov V E et al Statisticheskaya Fizika Plotnykh Gazov I Neideal’noi Plazmy (Statistical Physics Of Dense Gases And Nonideal Plasma) (Moscow: Fizmatlit, 2020)
Likalter A A Transport And Optical Properties Of Nonideal Plasma (Eds G A Kobzev, I T Iakubov, M M Popovich) (New York: Plenum Press, 1995) p. 133
Baranger M, Mozer B Phys. Rev. 115 521 (1959)
Mozer B, Baranger M Phys. Rev. 118 626 (1960)
Griem H R Spectral Line Broadening By Plasmas (New York: Academic Press, 1974)
Kalman G Phys. Fluids 4 300 (1961)
Romanovsky M Yu Phys. Lett. A 249 99 (1998)
Romanovsky M Yu, Ebeling W Contrib. Plasma Phys. 47 345 (2007)
Romanov A S, Chukbar K V Issled. Rossii 8 1650 (2005)
Wesenberg J H, Mølmer K Phys. Rev. Lett. 93 143903 (2004)
Romanovsky M Yu Physica A 265 264 (1999)
Lévy P Processus Stochastiques Et Mouvement Brownien (Paris: Gauthier-Villars, 1948)
Romanovsky M Yu Physica A 287 450 (2000)
Mantegna R N , Stanley H E Nature 383 587 (1996)
Sokolov I M Phys. Rev. E 63 011104 (2000)
Romanovsky M Yu Aktual’nye Problemy Statisticheskoi Radiofiziki (Malakhovskii Sbornik). Modern Problems Of Statistical Physics Vol. 1 (Nizhny Novgorod: Talam, 2002) p. 130
Romanovsky M Yu, Ebeling W, Schimansky-Geier L J. Phys. Conf. Ser. 11 99 (2005)
Landau L D, Lifshitz E M The Classical Theory Of Fields (Oxford: Pergamon Press, 1987); Translated from Russian, Landau L D, Lifshitz E M Teoriya Polya (Moscow: Fizmatlit, 2003)
Abramowitz M, Stegun I A (Eds) Handbook Of Mathematical Functions With Formulas, Graphs, And Mathematical Tables (United States. National Bureau of Standards. Applied Mathematics Series, 55) (New York: Dover Publ., 1964); Translated into Russian, Abramowitz M, Stegun I A (Eds) Spravochnik Po Spetsial’nym Funktsiyam S Formulami, Grafikami I Matematicheskimi Tablitsami (Moscow: Nauka, 1979)
Bohr A, Mottelson B R Nuclear Structure Vol. 1 Single-Particle Motion (New York: W.A. Benjamin, 1969); Translated into Russian, Bohr A, Mottelson B R Struktura Atomnogo Yadra Vol. 1 Odnochastichnoe Dvizhenie (Moscow: Nauka, 1971)
Stratonovich R L Sov. Phys. JETP 4 891 (1957); Stratonovich R L Zh. Eksp. Teor. Fiz. 31 1012 (1956)
Stratonovich R L Sov. Phys. JETP 5 1206 (1957); Stratonovich R L Zh. Eksp. Teor. Fiz. 32 1483 (1957)
Bunkin F V, Kadomtsev B B, Klimontovich Yu L, Koroteev N I, Landa P S, Maslov V P, Romanovskii Yu M "In memory of Ruslan Leont’evich Stratonovich" Phys. Usp. 40 751 (1997); Bunkin F V, Kadomtsev B B, Klimontovich Yu L, Koroteev N I, Landa P S, Maslov V P, Romanovskii Yu M "Pamyati Ruslana Leont’evicha Stratonovicha" Usp. Fiz. Nauk 167 789 (1997)