长程相关随机振荡积分的收敛性及其在均匀化中的应用

Stochastic homogenization of degenerate integral functionals with linear growth

We study the limit behaviour of a sequence of non-convex, vectorial, random integral functionals, defined on $W^{1,1}$, whose integrands satisfy degenerate linear growth conditions. These involve suitable random, scale-dependent weight-functions. Under minimal assumptions on the integrand and on the weight-functions, we show that the sequence of functionals homogenizes to a non-degenerate functional defined on $BV$.

Infinite server queues in a random fast oscillatory environment

In this paper, we consider a $G_t/G_t/\infty$ infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account some small time scale variations often observed in practice. We show a homogenization property for this system, which yields an approximation by a $M_t/G_t/\infty$ queue with modified parameters. Our limiting results include the description of the number of active servers, the total accumulated input and the solution of the storage equation. Hence in the fa…

随机介质中Levy过程驱动的随机微分方程的临界均匀化

Critical homogenization of Levy process driven SDEs in random medium

本文研究了在临界情形下，由Poisson随机测度和布朗运动驱动的具有平稳系数的随机微分方程的均匀化问题.我们陈述一个退火收敛定理。这个问题与积分偏微分方程的均匀化有很深的联系

具有凸增长的非凸无界积分泛函的随机均匀化

Stochastic homogenization of nonconvex unbounded integral functionals with convex growth

我们考虑随机积分泛函的均匀化问题。当被积函数具有标准增长条件时，定性理论是很好理解的。当涉及到无界泛函时，也就是说，当被积函数的区域不是整个空间并且可能依赖于空间变量时，没有令人满意的理论。在这方面的贡献，我们发展了一个完整的定性随机均匀化理论的非凸无界泛函凸增长。我们首先证明，如果被积函数是凸的，并有$p$ -增长从下面（与$p>d$，尺寸），那么它承认均匀化，无论从上面的增长条件。这个结果，关键依赖于存在和次线性在无穷远的校正，也是新的周期性的情况下。在非凸被积函数的情况下，我们证明了一个类似的均匀化结果持有提供的非凸被积函数承认一个凸被积函数（其域可能取决于空间变量），本身承认均匀化的双边估计。这一结果是感兴趣的严格推导橡胶弹性聚合物物理，其中包括随机均匀化的无界泛函。

Orlicz-Sobolev空间中一类极小化问题的随机-周期均匀化

Stochastic-Periodic Homogenization of a Class of Minimization Problems in Orlicz-Sobolev Spaces

本文在Orlicz-Sobolev空间中发展随机双尺度收敛方法，证明一类高振荡极小化问题的极小化子收敛到均匀化问题的极小化子。

Orlicz-Sobolev 空间中均值随机双尺度收敛及其在积分泛函均质化中的应用

Stochastic two-scale convergence in the mean in Orlicz-Sobolev's spaces and applications to the homogenization of an integral functional

本文研究了 Orlicz-Sobolev 空间中具有凸且非标准增长被积函数的积分泛函的随机均质化，将均值双尺度收敛的经典紧性结果推广至该空间，并证明了一类高度振荡极小化问题序列的极小值点收敛于均质化问题的极小值点。

Homogenization of iterated singular integrals with applications to random quasiconformal maps

We study homogenization of iterated randomized singular integrals and homeomorphic solutions to the Beltrami differential equation with a random Beltrami coefficient. More precisely, let $(F_j)_{j \geq 1}$ be a sequence of normalized homeomorphic solutions to the planar Beltrami equation $\overline{\partial} F_j (z)=μ_j(z,ω) \partial F_j(z),$ where the random dilatation satisfies $|μ_j|\leq k<1$ and has locally periodic statistics, for example of the type $$μ_j (z,ω)=ϕ(z)\sum_{n\in \mathbf{Z}^2}g(2^j z-n,X_{n}(ω)), $$ where $g(z,ω)$ decays rapidly in $z$, the random variables $X_{n}$ are i.i.d…

某些非线性积分-微分方程的随机均匀化

Stochastic Homogenization for Some Nonlinear Integro-Differential Equations

针对一类具有振荡系数的非线性非局部椭圆型方程，将周期均匀化结果推广到随机平稳遍历情形，证明了有效方程的存在性及原方程解的收敛性。