Discrete-time Simulation of Stochastic Volterra Equations

具有弱奇异核的随机 Volterra 积分方程的随机化 Milstein 格式

The randomized Milstein scheme for stochastic Volterra integral equations with weakly singular kernels

针对漂移系数不可微的弱奇异核随机 Volterra 积分方程，提出随机化 Milstein 格式，并借助随机化求积与 Riemann–Stieltjes 积分完成误差分析和数值模拟。

用于随机Lotka-Volterra捕食者-猎物模型的随机正保结构辛分裂方法

Stochastic positivity-preserving symplectic splitting methods for stochastic Lotka--Volterra predator-prey model

本文提出两种随机正保结构辛方法，用于求解随机Lotka-Volterra捕食者-猎物模型，证明其保持正性并具有离散辛守恒律，通过数值实验验证理论结果。

随机K辛积分器用于随机非规范哈密顿系统及其在洛特卡-沃勒特模型中的应用

Stochastic K-symplectic integrators for stochastic non-canonical Hamiltonian systems and applications to the Lotka--Volterra model

本文提出随机K辛积分器用于保持洛特卡-沃勒特模型解的正性，通过K辛条件保证数值方案保持原系统几何结构，验证了在L^1(Ω)意义下的一阶条件。

用小波方法求解二维线性随机Volterra积分方程的近似解

Approximation solution of two-dimensional linear stochastic Volterra integral equation by applying the Haar wavelet

本文提出基于Haar小波的高效方法，用于求解二维线性随机Volterra积分方程，并通过实例验证了方法的准确性。

基于Chelyshkov多项式求解随机Itô-Volterra积分方程的两种高效数值技术比较

Comparison of two efficient numerical techniques based on Chelyshkov polynomial for solving stochastic Itô-Volterra integral equation

本文比较了基于正交Chelyshkov多项式的谱配点法和谱Galerkin法求解非线性随机Itô-Volterra积分方程，通过Newton法求解转化后的非线性代数方程组，并验证了收敛性与有效性。

Numerical methods for stochastic Volterra integral equations with weakly singular kernels

In this paper, we first establish the existence, uniqueness and Hölder continuity of the solution to stochastic Volterra integral equations with weakly singular kernels. Then, we propose a $θ$-Euler-Maruyama scheme and a Milstein scheme to solve the equations numerically and we obtain the strong rates of convergence for both schemes in $L^{p}$ norm for any $p\geq 1$. For the $θ$-Euler-Maruyama scheme the rate is $\min\{1-α,\frac{1}{2}-β\}~ % (0<α<1, 0< β<\frac{1}{2})$ and for the Milstein scheme the rate is $\min\{1-α,1-2β\}$ when $α\neq \frac 12$, where $(0<α<1, 0< β<\frac{1}{2})$. These resu…