Abstract
Our study aims to specify the asymptotic error distribution in the discretization of a stochastic Volterra equation with a fractional kernel. It is well known that for a standard stochastic differential equation, the discretization error, normalized with its rate of convergence , converges in law to the solution of a certain linear equation. Similar to this, we show that a suitably normalized discretization error of the Volterra equation converges in law to the solution of a certain linear Volterra equation with the same fractional kernel.
Acknowledgments
The authors are grateful to Yushi Hamaguchi for helpful discussions, and to anonymous referees for their careful reading and suggestions.
Citation
Masaaki Fukasawa. Takuto Ugai. "Limit distributions for the discretization error of stochastic Volterra equations with fractional kernel." Ann. Appl. Probab. 33 (6B) 5071 - 5110, December 2023. https://doi.org/10.1214/23-AAP1941
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