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2008 Decay Rates of Solutions of Linear Stochastic Volterra Equations
David Reynolds, John Appleby
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Electron. J. Probab. 13: 922-943 (2008). DOI: 10.1214/EJP.v13-507


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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David Reynolds. John Appleby. "Decay Rates of Solutions of Linear Stochastic Volterra Equations." Electron. J. Probab. 13 922 - 943, 2008.


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

zbMATH: 1188.45008
MathSciNet: MR2413289
Digital Object Identifier: 10.1214/EJP.v13-507

Primary: 4K20
Secondary: 34K50 , 45D05 , 60H10 , 60H20

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

Vol.13 • 2008
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