论文标题
随机Volterra方程的离散时间模拟
Discrete-time Simulation of Stochastic Volterra Equations
论文作者
论文摘要
我们研究了随机燃烧方程的离散时间仿真方案，即欧拉和米尔斯坦方案，以及相应的多级蒙特卡罗方法。通过使用并适应张[22]的一些结果，并与Garsia-Rodemich-Rumsey引理一起，我们在超级规范下获得了Euler方案的收敛速率和Milstein方案的收敛速率。然后，我们应用这些方案以通过（多级）蒙特卡罗方法近似此类伏特拉方程的功能的期望，并计算它们的复杂性。
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.
