Shaikhet, L. Stability in probability of nonlinear stochastic hereditary systems. (English) Zbl 0831.60075 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) Cited in 18 Documents MSC: 60H20 Stochastic integral equations Keywords:stochastic hereditary systems; stability in probability; Volterra population equation PDF BibTeX XML Cite \textit{L. Shaikhet}, Dyn. Syst. Appl. 4, No. 2, 199--204 (1995; Zbl 0831.60075)