Decay Rates of Solutions of Linear Stochastic Volterra Equations
David W Reynolds, Dublin City University
John A. D. Appleby, Dublin City University
Abstract
The paper studies the exponential and non--exponential convergence rate to zero
of solutions of scalar linear convolution Ito-Volterra equations
in which the noise intensity depends linearly on the current state. By exploiting
the positivity of the solution, various upper and lower bounds in first mean and
almost sure sense are obtained, including Liapunov exponents.
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