Dirichlet forms methods, an application to the propagation of the error due to the Euler scheme

具有奇异核的Volterra型McKean-Vlasov随机微分方程：适定性、混沌传播与Euler格式

Volterra type McKean-Vlasov SDEs with singular kernels: Well-posedness, Propagation of Chaos and Euler schemes

本文研究奇异核Volterra型McKean-Vlasov SDE，建立了适定性，证明了带显式收敛率的混沌传播，并提出了粒子系统的显式Euler格式。

On a 2D stochastic Euler equation of transport type: existence and geometric formulation

We prove weak existence of Euler equation (or Navier-Stokes equation) perturbed by a multiplicative noise on bounded domains of $\mathbb R^2$ with Dirichlet boundary conditions and with periodic boundary conditions. Solutions are $H^1$ regular. The equations are of transport type.

Euler's scheme of Mckean-Vlasov SDEs with non-Lipschitz coefficients

In this paper, we show the strong well-posedness of Mckean-Vlasov SDEs with non-Lipschitz coefficients. Moreover, propagation of chaos and the convergence rate for Euler's scheme of Mckean-Vlasov SDEs are also obtained.

欧拉-马尔可夫方法用于乘性分数布朗运动驱动的分布依赖随机微分方程

Euler-Maruyama method for distribution dependent stochastic differential equation driven by multiplicative fractional Brownian motion

本文研究了由乘性分数布朗运动驱动的分布依赖随机微分方程的欧拉-马尔可夫方法，推导了误差上界并验证了其正确性。

Differential calculus for Dirichlet forms : the measure-valued gradient preserved by image

In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $Γ$ -- i.e. error structures -- and we are looking for an object related to $Γ$ which is linear and with a good behaviour by images. For this we introduce a new notion called the measure valued gradient which is a randomized square root of $Γ$. The exposition begins with inspecting some natural notions candidate to solve the problem before proposing the measure-valued gradient and proving its satisfactory properties.

全超线性增长 McKean-Vlasov SDE 及其粒子系统的驯服 Euler 逼近：强混沌传播、收敛性与遍历性的尖锐速率

Tamed Euler approximation for fully superlinear growth McKean-Vlasov SDE and their particle systems: sharp rates for strong propagation of chaos, convergence and ergodicity

针对全变量超线性增长的 McKean–Vlasov SDE 及粒子系统，论文提出全显式驯服 Euler 格式，证明适定性、维数一致的 N^{-1/2} 混沌传播速率、1/2 强收敛速率及指数遍历性。