Speciality:
05.13.18 (Mathematical modelling, calculating methods, and the program systems)
Phone: +7 (499) 263 66 40
Fax: +7 (499) 267 98 93
E-mail: Website: https://hoster.bmstu.ru/~kalinkin Keywords: Markov processes with the denumerable states,
exact solutions of the linear Kolmogorov equations,
the third (nonlinear) equation for the transition probabilities,
interacting particle system.
UDC: 519.2, 519.218.27, 531.19
MSC: 60g05, 60j25, 60j80, 60k35, 82c22
Subject:
Markov processes with a countable number of states are considered treated as multitype particle systems with group interaction. The result of a group interaction does not depend on the behavior of the remaining particles of the system. The machinery of multivariate generating functions is used to find the exact solutions of the first and second Kolmogorov systems of differential equations for transition probabilities. Applications of analytical methods are given to study real processes of particles transformations in various fields of science.
Main publications:
Sevastyanov B. A., Kalinkin A. V., “Random branching processes with interaction of particles”, Doklady Akademii Nauk SSSR, 264:2 (1982), 306–308; Soviet Math. Dokl., 25:3 (1982), 644–646
Kalinkin A. V., “Stationary distribution of a system of interacting particles with discrete states”, Doklady Akademii Nauk SSSR, 268:6 (1983), 1362–1364; Soviet Phys. Dokl., 28:2 (1983), 142–143
Kalinkin A. V., “Final probabilities for a random branching process with interaction of particles”, Doklady Akademii Nauk SSSR, 269:6 (1983), 1309–1312; Soviet Math. Dokl., 27:2 (1982), 493–497
Kalinkin A. V., “Branching processes with interaction of particles”, Probability and Mathematical Statistics: Encyclopedia, Scientific Publishers “Great Russian Encyclopedia”, Moscow, 1999, 104
Kalinkin A. V., “The de Finetti-Khinchin symmetry theorem in nonequilibrium statistical physics”, Doklady RAN, 370:4 (2000), 457–460; Doklady Mathematics, 61:1 (2000), 130–133
; Soviet Math. Dokl., 25:3 (1982), 
; Soviet Phys. Dokl., 28:2 (1983), 