Discrete-time Simulation of Stochastic Volterra Equations
Numerical Analysis
2022-03-08 v3 Numerical Analysis
Probability
Abstract
We study discrete-time simulation schemes for stochastic Volterra equations, namely the Euler and Milstein schemes, and the corresponding Multi-Level Monte-Carlo method. By using and adapting some results from Zhang [22], together with the Garsia-Rodemich-Rumsey lemma, we obtain the convergence rates of the Euler scheme and Milstein scheme under the supremum norm. We then apply these schemes to approximate the expectation of functionals of such Volterra equations by the (Multi-Level) Monte-Carlo method, and compute their complexity.
Cite
@article{arxiv.2004.00340,
title = {Discrete-time Simulation of Stochastic Volterra Equations},
author = {Alexandre Richard and Xiaolu Tan and Fan Yang},
journal= {arXiv preprint arXiv:2004.00340},
year = {2022}
}