Skwara, Urszula A stochastic symbiosis model with degenerate diffusion process. (English) Zbl 1223.47043 Ann. Pol. Math. 98, No. 2, 111-128 (2010). 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)]. Reviewer: Thomas Hagen (Memphis) Cited in 4 Documents 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) Keywords:symbiosis model; diffusion process; Markov semigroup; asymptotic stability Citations:Zbl 1204.47049 PDFBibTeX XMLCite \textit{U. Skwara}, Ann. Pol. Math. 98, No. 2, 111--128 (2010; Zbl 1223.47043) Full Text: DOI