Email this article Model of a stochastic process in the space of random joint events
- Authors: Biryukov A.A.1
-
Affiliations:
- Samara State Transport University
- Issue: Vol 25, No 4 (2021)
- Pages: 787-796
- Section: Short Communications
- URL: https://journal-vniispk.ru/1991-8615/article/view/72108
- DOI: https://doi.org/10.14498/vsgtu1865
- ID: 72108
Cite item
Full Text
Abstract
A model of the space of random joint events is being constructed. In space, along with the existence of a symmetric difference of joint events, a new postulate is introduced about the existence of a symmetric sum of random joint events. In the generated space, the stochastic equation of motion of the system and the expression for the probabilities of the system's transition between two events are modeled. The transition probability depends on the probabilities of compatibility of two, three, etc. events. The equation is equivalent to the Markov chain equation for incompatible events. The equation is equivalent to the equation of quantum theory if the events are compatible only in pairs.
Full Text
##article.viewOnOriginalSite##About the authors
Alexandr A. Biryukov
Samara State Transport University
Author for correspondence.
Email: biryukov_1@mail.ru
ORCID iD: 0000-0003-3955-1726
SPIN-code: 8103-9438
Scopus Author ID: 7006918751
http://www.mathnet.ru/person25619
Cand. Phys. & Math. Sci.; Professor; Dept. of Natural Sciences
2 V, Svobody st., Samara, 443066, Russian FederationReferences
- Morozov A. N., Skripkin A. V. Nemarkovskie fizicheskie protsessy [Non-Markovian Physical Processes]. Moscow, Fizmatlit, 2018, 288 pp. (In Russian)
- Skorobogatov G. A., Svertilov S. I. Quantum mechanics can be formulated as a non-Markovian stochastic process, Phys. Rev. A, 1998, vol. 58, no. 5, pp. 3426–3432. https://doi.org/10.1103/PhysRevA.58.3426.
- Popov N. N. Elementy teorii kvantovykh veroiatnostei [Elements of the Theory of Quantum Probabilities]. Moscow, Computing Center of RAS, 1996, 206 pp. (In Russian)
- Holevo A. S. Probabilistic and Statistical Aspects of Quantum Theory. Pisa, Edizioni della Normale, 2011, xvi+223 pp. https://doi.org/10.1007/978-88-7642-378-9
- Khrennikov A. Yu. Nekolmogorovskie teorii veroiatnostei i kvantovaia fizika [Non-Kolmogorovian Probability Theory in Quantum Physics]. Moscow, Fizmatlit, 2003, 207 pp.
- Ryazanov G. V. Quantum-mechanical probabilities as sums over paths, Sov. Phys., JETP, 1959, vol. 8, no. 1, pp. 85–93.
- Biryukov A. A. Markov chains for compatible states and the equations of quantum mechanics, Theor. Math. Phys., 1971, vol. 7, no. 1, pp. 364–367. https://doi.org/10.1007/BF01028134
- Biryukov A. A. Markovian processes for compatible events and equations of quantum mechanics, Vestn. Samar. Gos. Univ., Estestvennonauchn. Ser., 2010, no. 4(78), pp. 137–144 (In Russian).
- Biryukov A. A. Stochastic processes in the space of random joint events and the equations of quantum mechanics, Theor. Phys., 2012, no. 13, pp. 56–76 (In Russian).
- Biryukov A. A. Description of the diffraction of particles in the space of random joint events, Theor. Phys., 2013, no. 14, pp. 77–87 (In Russian).
- Biryukov A. A. Equations of quantum theory in the space of randomly joint quantum events, EPJ Web Conf., 2019, vol. 222, 03005. https://doi.org/10.1051/epjconf/201922203005
- Kolmogorov A. N. Osnovnye poniatiia teorii veroiatnostei [Basic Concepts of Probability Theory]. Moscow, Nauka, 1974, 120 pp. (In Russian)
- Rozanov Yu. A. Lektsii po teorii veroiatnostei [Lectures on Probability Theory]. Moscow, Nauka, 1968, 120 pp. (In Russian)
- Prokhorov A. V., Ushakov V. G., Ushakov N. G. Zadachi po teorii veroiatnosti [Problems on the Theory of Probability]. Moscow, Nauka, 1986, 328 pp. (In Russian)
- Biryukov A. A., Degtyareva Yu. V., Shleenkov M. A. Calculating the probabilities of quantum transitions in atoms and molecules numerically through functional integration, Bull. Russ. Acad. Sci. Phys., 2018, vol. 82, no. 12, pp. 1565–1569. https://doi.org/10.3103/S1062873818120055
Supplementary files
