Limit error distributions of Milstein scheme for stochastic Volterra equations with singular kernels
For stochastic Volterra equations driven by standard Brownian and with singular kernels K(u)=uH−1 2∕Γ(H+1∕2),H∈(0,1∕2), it is known that the Milstein scheme has a convergence rate of n−2H. In this paper, we show that this rate is optimal. Moreover, we show that the error normalized by n−2H converge stably in law to the (nonzero) solution of a certain linear Volterra equation of random coefficients with the same fractional kernel.
Authors
- Shanqi Liu (ORCID: https://orcid.org/0000-0002-5431-0448)
- Hong‐Jun Gao (ORCID: https://orcid.org/0000-0002-6766-0623)
- Yaozhong Hu (ORCID: https://orcid.org/0000-0003-4977-6099)
Institutions
- Nanjing Normal University (CN)
- University of Alberta (CA)
- Southeast University (CN)
Publication Details
- Journal
- Electronic Journal of Probability
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1214/25-ejp1386
- Primary Topic
- Stochastic processes and financial applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- University of Alberta
- National Natural Science Foundation of China
- China Scholarship Council
- Natural Sciences and Engineering Research Council of Canada