This paper studies the oscillatory properties of solutions of linear scalar stochastic delay differential equations with multiplicative noise. It is shown that such noise will induce an oscillation in the solution whenever there is negative feedback from the delay term. The zeros of the process...

This paper studies the oscillatory properties of solutions of linear scalar stochastic delay differential equations with multiplicative noise. It is shown that such noise will induce an oscillation in the solution whenever there is negative feedback from the delay term. The zeros of the process...

We study convergence rates to zero of solutions of the scalar equationwhere f, g, h are globally Lipschitz, xg(x)0 for nonzero x, and k is continuous, integrable, positive and limt--[infinity] k(t-s)/k(t)=1, for s0. Thenfor nontrivial solutions satisfying limt--[infinity] X(t)=0 on A, a set of...

This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised. Connections with the class of ARCH($\infty$) processes are sketched.

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