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A stochastic symbiosis model with degenerate diffusion process. (English) Zbl 1223.47043
The author investigates a 2D system of stochastic differential equations modeling the dynamics of two species in symbiosis. Two cases of stochastic perturbation are considered: in the first case, both diffusion coefficients are positive, while in the second case, one coefficient is positive and the other one vanishes. Well-posedness, positivity and long-term behavior of solutions is studied. The results presented extend earlier work [Ann. Pol. Math. 97, No. 3, 257–272 (2010; Zbl 1204.47049)].

MSC:
47D07 Markov semigroups and applications to diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
92D25 Population dynamics (general)
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