The paper is focused on the analysis of stability properties of a family of numerical methods designed for the numerical solution of stochastic Volterra integral equations. Stability properties are provided with respect to the basic test equation, as well as to the convolution test equation. For each equation, stability properties are intended both in the mean-square and in the asymptotic sense. Stability regions are also provided for a selection of methods. Numerical experiments confirming the theoretical study are also given.
On the stability of ϑ-methods for stochastic Volterra integral equations
Conte, Dajana;Paternoster, Beatrice
2018-01-01
Abstract
The paper is focused on the analysis of stability properties of a family of numerical methods designed for the numerical solution of stochastic Volterra integral equations. Stability properties are provided with respect to the basic test equation, as well as to the convolution test equation. For each equation, stability properties are intended both in the mean-square and in the asymptotic sense. Stability regions are also provided for a selection of methods. Numerical experiments confirming the theoretical study are also given.File in questo prodotto:
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2018 On the stability of theta-methods for stochastic Volterra integral equations, Discr. Cont. Dyn. Sys. - B 23(7), 2695-2708 (2018).pdf
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