A class of nonlinear processes admitting complete study
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 55-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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A sample of a nonlinear random walk on the discrete line $\mathbb{Z}$ is considered. It is shown that for some choice of parameters it possesses certain properties absent in the classic case. For example, it has a one-parametric family of invariant measures and a motion integral.
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S. A. Muzychka. A class of nonlinear processes admitting complete study. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 55-57. http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a9/

[1] Kats M., Neskolko veroyatnostnykh zadach fiziki i matematiki, Nauka, M., 1976

[2] Antunes N., Fricker C., Robert P., Tibi D., “Stochastic networks with multiple stable points”, Ann. Probab., 36:1 (2008), 255–278 | DOI | MR | Zbl

[3] Bena M., Le Boudec J., “A class of mean field interaction models for computer and communication systems”, Performance Evaluation, 65:11 (2008), 823–838

[4] Rybko A., Shlosman S., “Poisson hypothesis for information networks”, Moscow Math. J., 5:3 (2005), 679–704 | MR | Zbl

[5] Kolokoltsov V., Nonlinear Markov processes and kinetic equations, Cambridge University Press, Cambridge, 2010 | MR | Zbl

[6] Sznitman A., Topics in propagation of chaos, Calcul des probabilites, Saint-Flour, 1989

[7] Benachour S., Roynette B., Talay D., Vallois P., “Nonlinear selfstabilizing processes. I: Existence, invariant probability, propagation of chaos”, Stochast. Proces. and Appl., 75:2 (1998), 173–201 | DOI | MR | Zbl

[8] Benachour S., Roynette B., Vallois P., “Nonlinear self-stabilizing processes. II: Convergence to invariant probability”, Stochast. Proces. and Appl., 75:2 (1998), 203–224 | DOI | MR | Zbl

[9] Bulinskii A.V., Shiryaev A.N., Teoriya sluchainykh protsessov, Fizmatlit, M., 2004

[10] Shiryaev A.N., “O martingalnykh metodakh v zadachakh o peresechenii granits brounovskim dvizheniem”, Sovremennye problemy matematiki, 8:1 (2007), 3–78 | DOI

[11] Muzychka S., Vaninsky K., “A class of nonlinear random walks related to the Ornstein–Uhlenbeck process”, Markov Processes and Related Fields, 17:2 (2012), 277–304 | MR

[12] Ligget T., Markovskie protsessy s lokalnym vzaimodeistviem, Mir, M., 1989 | MR

[13] Iosida K., Funktsionalnyi analiz, Mir, M., 1967 | MR