平面上高斯密度的指数为2的随机匹配

Euclidean random matching in 2D for non-constant densities

We consider the 2-dimensional random matching problem in $\mathbb{R}^2.$ In a challenging paper, Caracciolo et. al. arXiv:1402.6993 on the basis of a subtle linearization of the Monge Ampere equation, conjectured that the expected value of the square of the Wasserstein distance, with exponent $2,$ between two samples of $N$ uniformly distributed points in the unit square is $\log N/2πN$ plus corrections, while the expected value of the square of the Wasserstein distance between one sample of $N$ uniformly distributed points and the uniform measure on the square is $\log N/4πN$. These conjectur…

随机PDE的转移密度的下估计和指数遍历性的界

Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDE's

利用Ornstein-Uhlenbeck桥给出了由无穷维随机方程定义的马尔可夫过程的转移密度公式，并给出了转移密度的一个有用的下界估计.因此，对一大类方程证明了一致指数遍历性和$V$ -遍历性.我们还提供了计算界的收敛速度和谱间隙的马尔可夫半群定义的方程。的界限变成是均匀的一个大家庭的非线性漂移系数。给出了有限维随机方程和半线性抛物型方程的例子。

Transition densities of spectrally positive Lévy processes

We prove asymptotic behaviour of transition density for a large class of spectrally one-sided Lévy processes of unbounded variation satisfying mild condition imposed on the second derivative of the Laplace exponent, or equivalently, on the real part of the characteristic exponent. We also provide sharp two-sided estimates on the density when restricted additionally to processes without Gaussian component.

Transition densities of subordinators of positive order

We prove existence and asymptotic behavior of the transition density for a large class of subordinators whose Laplace exponents satisfy lower scaling condition at infinity. Furthermore, we present lower and upper bounds for the density. Sharp estimates are provided if additional upper scaling condition on the Laplace exponent is imposed. In particular, we cover the case when the (minus) second derivative of the Laplace exponent is a function regularly varying at infinity with regularity index bigger than -2.

Standardizing densities on Gaussian spaces

In the present note we investigate the problem of standardizing random variables taking values on infinite dimensional Gaussian spaces. In particular, we focus on the transformations induced on densities by the selected standardization procedure. We discover that, under certain conditions, the Wick exponentials are the key ingredients for treating this kind of problems.

Lévy过程分布密度的内禀小时间估计

Intrinsic small time estimates for distribution densities of Lévy processes

我们构造了Lévy过程在小时间内的转移概率密度的内在对角和非对角上、下估计.所谓内禀，我们的意思是这样的估计反映了过程的特征指数的结构。本文所用的技术依赖于各自的特征函数的傅里叶逆变换的渐近分析。我们提供了几个例子，特别是，相当不规则的Lévy测度，以说明我们的结果。