Discrete-time Simulation of Stochastic Volterra Equations

Alexandre Richard (1, 2) , Xiaolu Tan (3) , Fan Yang (3)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 Fédération de Mathématiques de CentraleSupélec
3 Department of Mathematics [CUHK]

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. We finally provide some numerical simulation results.

Domaines: Analyse numérique [math.NA]; Probabilités [math.PR]

Alexandre Richard, Xiaolu Tan, Fan Yang. Discrete-time Simulation of Stochastic Volterra Equations. Stochastic Processes and their Applications, 2021, ⟨10.1016/j.spa.2021.07.003⟩. ⟨hal-02528983⟩