Two approaches that allow to construct a probabilistic representation of a generalized solution of the Cauchy problem for a system of quasilinear parabolic equations are proposed. The system under consideration describes a population dynamics model for a prey-predator population. The stochastic problem associated with this parabolic system is presented in two forms, which give a way to derive the required probabilistic representation. Bibliography: 16 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 431, 2014, pp. 9–36.
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Belopolskaya, Y.I. Probabilistic Model for the Lotka-Volterra System with Cross-Diffusion. J Math Sci 214, 425–442 (2016). https://doi.org/10.1007/s10958-016-2787-0
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DOI: https://doi.org/10.1007/s10958-016-2787-0