Work

Limit error distributions of Milstein scheme for stochastic Volterra equations with singular kernels

Year: 2025

Type: article

Abstract: 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.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1386

Authors: Shanqi Liu, Yaozhong Hu, Hongjun Gao

Institutions: Nanjing Normal University, University of Alberta, Southeast University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: University of Alberta, National Natural Science Foundation of China, China Scholarship Council, Natural Sciences and Engineering Research Council of Canada