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The improved results on the stochastic Kolmogorov system with time-varying delay

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  • This paper discusses the stochastic Kolmogorov system with time-varying delay. Under two classes of sufficient conditions, this paper solves the non-explosion, the moment boundedness and the polynomial pathwise growth simultaneously. This is an important improvement for the existing results, since the moment boundedness and the polynomial pathwise growth do not imply each in general. Moreover, these two classes of conditions only depends on the parameters of the system and are easier to be used. Finally, a two-dimensional Komogorov model is examined to illustrate the efficiency of our result.
    Mathematics Subject Classification: Primary: 60H10, 34A34, 34D40, 34K50.

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