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Stochastic delay population systems. (English) Zbl 1216.60051
The author is interested in the solution of the stochastic delay population system (SDPS) $$dx(t)= \text{diag}(x_1(t),\dots,x_n(t))([b(t)+A(t)x(t)+G(t)x(t-\tau)]dt+\sigma(t)dw(t)) $$ where all coefficients are locally Lipschitz continuous. His main result is a new sufficient condition for the existence of a global positive solution which depends on the matrix $A(t)$ but not on $G(t)$. Some new asymptotic properties for the moments as well as for the sample paths of the solution are also established. In particular, ultimate boundedness and extinction are discussed.

60H10Stochastic ordinary differential equations
60J65Brownian motion
34K40Neutral functional-differential equations
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