单调梯度方程组逼近的收敛性

On the convergence of monotone schemes for path-dependent PDE

We propose a reformulation of the convergence theorem of monotone numerical schemes introduced by Zhang and Zhuo for viscosity solutions of path-dependent PDEs, which extends the seminal work of Barles and Souganidis on the viscosity solution of PDE. We prove the convergence theorem under conditions similar to those of the classical theorem in the work of Barles and Souganidis. These conditions are satisfied, to the best of our knowledge, by all classical monotone numerical schemes in the context of stochastic control theory. In particular, the paper provides a unified approach to prove the co…

The random periodic solution of a stochastic differential equation with a monotone drift and its numerical approximation

In this paper we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler-Maruyama method. The existence of the random periodic solution is shown as the limits of the pull-back flows of the SDE and discretized SDE respectively. We establish a convergence rate of the strong error for the backward Euler-Maruyama method and obtain the weak convergence result for the approximation of the periodic measu…

Large deviations for locally monotone stochastic partial differential equations driven by Levy noise

In this paper, we establish a large deviation principle for a type of stochastic partial differential equations (SPDEs) with locally monotone coefficients driven by Lévy noise. The weak convergence method plays an important role.

Multivalued Monotone Stochastic Differential Equations with Jumps

We study multivalued stochastic differential equations (MSDEs) with maximal monotone operators driven by semimartingales with jumps. We discuss in detail some methods of approximation of solutions of MSDEs based on discretization of processes and Yosida approximation of the monotone operator. We also study the general problem of stability of solutions of MSDEs with respect to the convergence of driving semimartingales.

单调随机微分方程向后欧拉格式的$L^p$收敛速度

$L^p$-Convergence Rate of Backward Euler Schemes for Monotone SDEs

该研究提出统一方法推导单调SDEs向后欧拉格式的$L^p(p\ge4)$强收敛速度，结果可应用于多项式增长系数SODEs的向后欧拉格式，并可推广至乘性迹类噪声驱动的同系数SPDEs的Galerkin向后欧拉格式。

G-方程的单调格式及其在鲁棒中心极限定理显式收敛速率中的应用

A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem

本文提出一种用于完全非线性PDE（G-方程）的递归单调近似格式，利用比较原理与磨光过程证明其收敛性并获得显式误差界，进而应用于推导Peng鲁棒中心极限定理的Berry-Esseen型收敛速率及Black-Scholes-Barenblatt方程的近似格式。

具有受控波动率的位移单调平均场博弈的定量收敛

Quantitative convergence for displacement monotone mean field games with controlled volatility

研究具有共同噪声和受控波动率的平均场博弈收敛问题，通过最大值原理将其转化为前向-后向混沌传播问题，并利用位移单调性首次为共同噪声受控博弈提供了开环Nash均衡的定量收敛证明。

关于扰动理论和具有非全局单调系数的随机常微分方程和偏微分方程的强收敛速率

On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients

本文提出了一种随机微分方程的扰动理论，用于估计解过程与任意伊藤过程之间的L^p距离，并应用该理论研究了非全局单调系数的随机常微分方程和随机偏微分方程的数值解的强收敛速率。

无穷小生成元的收敛性与凸单调半群的稳定性

Convergence of infinitesimal generators and stability of convex monotone semigroups

本文研究了强连续凸单调半群在连续函数空间上的稳定性，通过混合拓扑中无穷小生成元的收敛性，提供了一个稳定性结果，不同于以往结果，本文不依赖粘性解理论，而是使用了一个最近的比较原理，通过定义在Lipschitz集上的Γ生成元唯一确定半群，从而类似于线性情况的经典结果。该框架还允许时间和空间的离散化，并涵盖了多种应用。