## Electronic Journal of Probability

### Decay Rates of Solutions of Linear Stochastic Volterra Equations

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 30, 922-943.

Dates
Accepted: 9 May 2008
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819103

Digital Object Identifier
doi:10.1214/EJP.v13-507

Mathematical Reviews number (MathSciNet)
MR2413289

Zentralblatt MATH identifier
1188.45008

Rights

#### Citation

Reynolds, David; Appleby, John. Decay Rates of Solutions of Linear Stochastic Volterra Equations. Electron. J. Probab. 13 (2008), paper no. 30, 922--943. doi:10.1214/EJP.v13-507. https://projecteuclid.org/euclid.ejp/1464819103

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