Limit distributions for the discretization error of stochastic Volterra equations
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 $1/\sqrt{n}$, converges in law to the solution of a certain linear equation. Similarly 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2021
- DOI:
- 10.48550/arXiv.2112.06471
- arXiv:
- arXiv:2112.06471
- Bibcode:
- 2021arXiv211206471F
- Keywords:
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- Mathematics - Numerical Analysis;
- Mathematics - Probability