scholarly journals Hölder Continuity for the Parabolic Anderson Model with Space-Time Homogeneous Gaussian Noise

2019 ◽  
Vol 39 (3) ◽  
pp. 717-730 ◽  
Author(s):  
Raluca M Balan ◽  
Lluís Quer-Sardanyons ◽  
Jian Song
Keyword(s):  
Anderson Model ◽  
Gaussian Noise ◽  
Hölder Continuity ◽  
Space Time ◽  
Parabolic Anderson Model ◽  
Holder Continuity

scholarly journals Hölder continuity for parabolic Anderson equation with non-Gaussian noise

2016 ◽  
Vol 441 (2) ◽  
pp. 684-691 ◽  
Author(s):  
Jianbo Cui ◽  
Zhihui Liu ◽  
Lijun Miao ◽  
Xu Wang
Keyword(s):  
Gaussian Noise ◽  
Hölder Continuity ◽  
Holder Continuity ◽  
Non Gaussian

scholarly journals HÖLDER CONTINUITY OF THE INTEGRATED DENSITY OF STATES FOR MATRIX-VALUED ANDERSON MODELS

2008 ◽  
Vol 20 (07) ◽  
pp. 873-900 ◽  
Author(s):  
HAKIM BOUMAZA
Keyword(s):  
Density Of States ◽  
Anderson Model ◽  
Final Section ◽  
Hölder Continuity ◽  
Regularity Result ◽  
Previous Article ◽  
Integrated Density Of States ◽  
Holder Continuity ◽  
Transfer Matrices ◽  
Anderson Models

We study a class of continuous matrix-valued Anderson models acting on L2(ℝd) ⊗ ℂN. We prove the existence of their Integrated Density of States for any d ≥ 1 and N ≥ 1. Then, for d = 1 and for arbitrary N, we prove the Hölder continuity of the Integrated Density of States under some assumption on the group GμE generated by the transfer matrices associated to our models. This regularity result is based upon the analoguous regularity of the Lyapounov exponents associated to our model, and a new Thouless formula which relates the sum of the positive Lyapounov exponents to the Integrated Density of States. In the final section, we present an example of matrix-valued Anderson model for which we have already proved, in a previous article, that the assumption on the group GμE is verified. Therefore, the general results developed here can be applied to this model.

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