Stability in probability of nonlinear stochastic hereditary systems. (English) Zbl 0831.60075

Shaikhet, L.

Dyn. Syst. Appl. 4, No. 2, 199-204 (1995).

It is shown that the examination of nonlinear stochastic hereditary systems (or systems given in terms of functional differential equations) with respect to stability in probability can be reduced to an examination of the mean square stability of linear systems. The results are illustrated by considering the Volterra population equation \[ \dot x(t)= rx(t)\Biggl[1- {1\over k} \int^\infty_0 x(t- s) dH(s)\Biggr]. \]

Reviewer: A.Dale (Durban)

MSC:

60H20

Stochastic integral equations

Keywords:

stochastic hereditary systems; stability in probability; Volterra population equation