Potential theory for hyperbolic SPDEs

关于由时空莱维白噪声驱动的超几何随机微分方程组的全局良好性问题

Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise

本文研究了由时空莱维白噪声驱动的超几何随机微分方程组在局部利普希茨和线性增长系数下的全局良好性问题。

Probability density for a hyperbolic SPDE with time dependent coefficients

We prove the existence and smoothness of density for the solution of a hyperbolic SPDE with free term coefficients depending on time, under hypoelliptic non degeneracy conditions. The result extends those proved in Cattiaux and Mesnager, PTRF 2002, to an infinite dimensional setting.

Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE

We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full $L^1$ setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an $L^1$-contraction property for the solutions.

矩形增量下的随机重构定理及其在混合双曲型SPDE中的应用

A Stochastic Reconstruction Theorem on Rectangular Increments with an Application to a Mixed Hyperbolic SPDE

该研究将随机重构定理推广至矩形增量情形，证明了结合Walsh随机积分与Young乘积的新型混合双曲型SPDE的适定性。

带加性噪声的半线性双曲型随机偏微分方程全离散有限元逼近的弱收敛性

Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise

本文针对加性噪声驱动的半线性随机波动方程，结合标准有限元空间离散与指数函数有理逼近时间离散，利用 Malliavin 分析证明弱收敛速率约为强速率的两倍，并通过数值模拟验证了理论结果。

Some linear SPDEs driven by a fractional noise with Hurst index greater than 1/2

In this article, we identify the necessary and sufficient conditions for the existence of a random field solution for some linear s.p.d.e.'s of parabolic and hyperbolic type. These equations rely on a spatial operator $\cL$ given by the $L^2$-generator of a $d$-dimensional Lévy process $X=(X_t)_{t \geq 0}$, and are driven by a spatially-homogeneous Gaussian noise, which is fractional in time with Hurst index $H>1/2$. As an application, we consider the case when $X$ is a $β$-stable process, with $β\in (0,2]$. In the parabolic case, we develop a connection with the potential theory of the Markov…