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Relative persistence for stochastic population models: Finite sample boundedness. (English) Zbl 0682.92018
Mathematical ecology, Proc. Autumn Course Res. Semin., Miramare- Trieste/Italy 1986, 753-772 (1988).
[For the entire collection see Zbl 0659.00019.]
The author uses stochastic differential equations of the form \[ dX_ i=X_ i[f_ i(X)dt+\sum^{m}_{j=1}g_{ij}(X)dW_ j],\quad 1\leq i\leq n, \] to describe multi-species population models. A condition called finite sample boundedness is proposed, to be satisfied by persistent populations. The condition requires that the probability of hitting 0 or \(\infty\) in finite time be zero. Some examples are discussed.
Reviewer: A.D.Barbour

MSC:
92D25 Population dynamics (general)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)