Geodesic
Chemotaxis stochastic model for two populations
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 37-63

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We construct a probabilistic representation of the Cauchy problem weak solution for a system of parabolic equations describing a chemotaxis process in a system of two interacting populations. We derive a stochastic system describing the Keller–Segel type chemotaxis process and the Lotka–Voltera type interatction between two populations and prove existence and uniqueness theorem for its solution. Finally, we show connections between solutions of the stochastic system and the Cauchy problem weak solution of the original PDE system. 
@article{ZNSL_2020_495_a2,
     author = {Ya. I. Belopolskaya and E. I. Nemchenko},
     title = {Chemotaxis stochastic model for two populations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {37--63},
     publisher = {mathdoc},
     volume = {495},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a2/}
}
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Ya. I. Belopolskaya; E. I. Nemchenko. Chemotaxis stochastic model for two populations. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 37-63. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a2/