On the equivalence of operator and combinatorial approaches for onestep random Markov processes
https://doi.org/10.29235/1561-2430-2022-58-1-21-33
Abstract
Herein, for one-step random Markov processes the comparison of the operator and combinatorial methods based on the use of functional integrals is performed. With the combinatorial approach, the transition from the stochastic differential equation to the functional integral is used. This allows us to obtain the expression for the mean population size in terms of the functional integral. With the operator approach, the transition to the functional integral is performed via the creation and annihilation operators. It is shown that the mean values calculated using the functional integrals arising in the combinatorial and operator approaches coincide.
Keywords
random Markov processes,
birth-death processes,
one-step processes,
combinatorial approach,
operator approach,
mean values,
functional integrals
Supporting agencies: The research was carried out under the financial support of the Belarusian Republican Foundation for Fundamental Research within the framework of Project no. Ф20МС-005.
About the Authors
E. A. Ayryan
Meshcheryakov Laboratory of Information Technologies, Joint Institute for Nuclear Research; State University «Dubna»; A. I. Alikhanyan National Science Laboratory
Russian Federation
Russian Federation
Edik A. Ayryan – Ph. D. (Physics and Mathematics), Head of Sector
6, Joliot-Curie Str., 141980, Dubna
19, Universitetskaja Str., 141980, Dubna
Yerevan, Republic of Armenia
M. Hnatic
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research; Institute of Experimental Physics, Slovak academy of Sciences; Faculty of Sciences, P. J. Šafárik University in Košice
Russian Federation
Russian Federation
Michal Hnatic – Dr. Sc. (Physics and Mathematics), Professor, Deputy Director
6, Joliot-Curie Str., Dubna
47, Watsonova Str., Košice, Slovak Republic
9, Park Angelinum, Košice, Slovak Republic
V. B. Malyutin
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Victor B. Malyutin – Dr. Sc. (Physics and Mathematics), Principal Researcher
11, Surganov Str., 220072, Minsk
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