当前位置: X-MOL 学术Potential Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Powers of Brownian Green Potentials
Potential Analysis ( IF 1.1 ) Pub Date : 2021-01-23 , DOI: 10.1007/s11118-020-09883-z
Claude Dellacherie , Mauricio Duarte , Servet Martínez , Jaime San Martín , Pierre Vandaele

In this article we study stability properties of \(g_{_{\mathcal {O}}}\!\), the standard Green kernel for \(\mathcal {O}\) an open regular set in \(\mathbb {R}^{d}\). In d ≥ 3 we show that \( g^{\beta }_{_{\mathcal {O}}}\) is again a Green kernel of a Markov Feller process, for any power β ∈ [1,d/(d − 2)). In dimension d = 2, we show the same result for \( g^{\beta }_{_{\mathcal {O}}}\), for any β ≥ 1 and for kernels \(\exp (\alpha g_{_{\mathcal {O}}}\!), \exp (\alpha g_{_{\mathcal {O}}}\!)-1\), for α ∈ (0,2π), when \(\mathcal {O}\) is an open Greenian regular set whose complement contains a ball.



中文翻译:

布朗绿色势能的力量

在本文中,我们研究\(g _ {_ {\ mathcal {O}}} \!\)的稳定性,这是\(\ mathcal {O} \)\(\ mathbb { R} ^ {d} \)。在d ≥3,我们表明,\(G ^ {\的β} _ {_ {\ mathcal {ö}}} \)再次是马尔可夫费勒处理的绿内核,对于任何功率β∈ [1,d /(d -2))。在尺寸d = 2,我们显示了相同的结果\(G ^ {\的β} _ {_ {\ mathcal {ö}}} \) ,对于任何β ≥1和用于内核\(\ EXP(\阿尔法G_ {_ {\ mathcal {O}}} \!),\ exp(\ alpha g _ {_ {\ mathcal {O}}} \!)-1 \),对于α∈(0,2 π),当\(\ mathcal {Ø} \)是一个开放的Greenian定期集,其补包含一个球。

更新日期:2021-01-24
down
wechat
bug