Geodesic
Jacobi branching random walks corresponding to orthogonal polynomials of discrete variable
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 173-188 
A. V. Lyulintsev. Jacobi branching random walks corresponding to orthogonal polynomials of discrete variable. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 173-188. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a11/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A branching random walk on $\mathbf{Z}_+$ is considered, which corresponds to a Jacobi matrix. Previously, formulas for the average number of particles at an arbitrary fixed point in $\mathbf{Z}_+$ at time $t>0$ were obtained in terms of the orthogonal polynomials associated with this matrix. In the present work, the application of the obtained results to certain models involving orthogonal polynomials of a discrete variable (Krawtchouk, Meixner, and Poisson–Charlier polynomials) is discussed.

[1] M. Domínguez de la Iglesia, Orthogonal Polynomials in the Spectral Analysis of Markov Processes, Cambridge University Press, Cambridge, 2022 | Zbl

[2] R. Aski, R. Roi, Dzh. Endryus, Spetsialnye funktsii, perevod s angl. pod red. Yu. A. Neretina, MTsNMO, M., 2013

[3] N. I. Akhiezer, Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s neyu, Gos. izd-vo fiz.-matem. lit-ry, M., 1961

[4] M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, ucheb. posobie, L., 1980

[5] I. I. Gikhman, A. V. Skorokhod, Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1977 | MR

[6] I. I. Gikhman, A. V. Skorokhod, Teoriya sluchainykh protsessov, v. II, Nauka, M., 1973

[7] A. V. Lyulintsev, “Markovskie vetvyaschiesya sluchainye bluzhdaniya po $\mathbf{Z}_+$. Podkhod s ispolzovaniem ortogonalnykh mnogochlenov. I”, Teoriya veroyatn. i ee primen., 69:1 (2024), 91–111 | DOI | Zbl

[8] A. V. Lyulintsev, “Markovskie vetvyaschiesya sluchainye bluzhdaniya po $\mathbf{Z}_+$. Podkhod s ispolzovaniem ortogonalnykh mnogochlenov. II”, Teoriya veroyatn. i ee primen., 69:3 (2024), 439–458 | DOI | Zbl

[9] A. V. Lyulintsev, “Markovskie vetvyaschiesya sluchainye bluzhdaniya po $\mathbf{Z}_+$ s pogloscheniem v nule”, Zap. nauchn. semin. POMI, 526, 2023, 109–129 | MR

[10] A. V. Lyulintsev, “Ob asimptoticheskom povedenii srednego znacheniya funktsionalov ot sluchainogo polya chastits, zadavaemogo vetvyaschimsya sluchainym bluzhdaniem”, Algebra i analiz, 36:4 (2024), 38–56

[11] G. Sege, Ortogonalnye mnogochleny, Gos. izd-vo fiz.-matem. lit-ry, M., 1962

[12] N. V. Smorodina, E. B. Yarovaya, “Ob odnoi predelnoi teoreme dlya vetvyaschikhsya sluchainykh bluzhdanii”, Teoriya veroyatn. i ee primen., 68:4 (2023), 779–795 | DOI | MR

[13] E. B. Yarovaya, Vetvyaschiesya sluchainye bluzhdaniya v neodnorodnoi srede, Izd-vo Tsentra prikl. issled. pri mekh.-matem. f-te MGU, M., 2007