Discrete-time Simulation of Stochastic Volterra Equations - Archive ouverte HAL
Article Dans Une Revue Stochastic Processes and their Applications Année : 2021

Discrete-time Simulation of Stochastic Volterra Equations

Résumé

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.

Dates et versions

hal-02528983 , version 1 (02-04-2020)

Identifiants

Citer

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⟩
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