Electronic Journal of Probability

Decay Rates of Solutions of Linear Stochastic Volterra Equations

David Reynolds and John Appleby

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 4K20
Secondary: 34K50: Stochastic functional-differential equations [See also , 60Hxx] 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations 45D05: Volterra integral equations [See also 34A12]

almost sure exponential asymptotic stability Liapunov exponent subexponential distribution subexponential function Volterra equations Ito-Volterra equations

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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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