Geodesic
A stochastic model for the Lotka--Volterra system with cross-diffusion
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 9-36

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We propose two approaches that allow to construct a probabilistic representation of a generalized solution of the Cauchy problem for a system of quasilinear parabolic equations. The system under consideration presents a population dynamics model for a prey-predator population. We construct two types of stochastic problem associated with this parabolic system that give the way to derive the required probabilistic representation. 
@article{ZNSL_2014_431_a1,
     author = {Ya. I. Belopolskaya},
     title = {A stochastic model for the {Lotka--Volterra} system with cross-diffusion},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {9--36},
     publisher = {mathdoc},
     volume = {431},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a1/}
}
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Ya. I. Belopolskaya. A stochastic model for the Lotka--Volterra system with cross-diffusion. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 9-36. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a1/