Markov processes with the denumerable states,
exact solutions of the linear Kolmogorov equations,
the third (nonlinear) equation for the transition probabilities,
interacting particle system.
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.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1978 (department of theory probability). Ph.D. thesis was defended in 1984. A list of my works contains more than 40 titles. I read the course of theory of Markov processes for students in Moscow State Bauman Technical University.
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
A. V. Kalinkin, “Absorption probability at the border of a random walk in a quadrant and a branching process with interaction of particles”, Teor. Veroyatnost. i Primenen., 47:3 (2002), 452–474; Theory Probab. Appl., 47:3 (2003), 469–487
A. V. Kalinkin, “Exact solutions of the Kolmogorov equations for critical branching processes with two complexes of interaction of particles”, Uspekhi Mat. Nauk, 56:3(339) (2001), 173–174; Russian Math. Surveys, 56:3 (2001), 586–588
A. V. Kalinkin, “On the Extinction Probability of a Branching Process with Two Kinds of Interaction of Particles”, Teor. Veroyatnost. i Primenen., 46:2 (2001), 376–380; Theory Probab. Appl., 46:2 (2002), 347–352
A. V. Kalinkin, “Final probabilities for a branching process with interaction of particles and an epidemic process”, Teor. Veroyatnost. i Primenen., 43:4 (1998), 773–780; Theory Probab. Appl., 43:4 (1999), 633–640
A. V. Kalinkin, “On the probability of the extinction of branching process with interaction of particles”, Teor. Veroyatnost. i Primenen., 27:1 (1982), 192–197; Theory Probab. Appl., 27:1 (1982), 201–205
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