Lyapunov exponent for the parabolic anderson model with lévy noise

2005 ◽  
Vol 132 (3) ◽  
pp. 321-355 ◽  
Author(s):  
M. Cranston ◽  
T. S. Mountford ◽  
T. Shiga
Keyword(s):  
Lyapunov Exponent ◽  
Anderson Model ◽  
Lévy Noise ◽  
Parabolic Anderson Model ◽  
Levy Noise

An ergodic theorem of a parabolic Anderson model driven by Lévy noise

2011 ◽  
Vol 6 (6) ◽  
pp. 1147-1183
Author(s):  
Yong Liu ◽  
Jianglun Wu ◽  
Fengxia Yang ◽  
Jianliang Zhai
Keyword(s):  
Ergodic Theorem ◽  
Anderson Model ◽  
Lévy Noise ◽  
Parabolic Anderson Model ◽  
Model Driven ◽  
Levy Noise

scholarly journals Lyapunov exponent for the parabolic Anderson model in Rd

2006 ◽  
Vol 236 (1) ◽  
pp. 78-119 ◽  
Author(s):  
M. Cranston ◽  
T.S. Mountford
Keyword(s):  
Lyapunov Exponent ◽  
Anderson Model ◽  
Parabolic Anderson Model

scholarly journals An Enhanced Intrinsic Time-Scale Decomposition Method Based on Adaptive Lévy Noise and Its Application in Bearing Fault Diagnosis

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 617
Author(s):  
Jianpeng Ma ◽  
Shi Zhuo ◽  
Chengwei Li ◽  
Liwei Zhan ◽  
Guangzhu Zhang
Keyword(s):  
Fault Diagnosis ◽  
Time Scale ◽  
Lévy Noise ◽  
Model Parameters ◽  
Rolling Bearings ◽  
Intrinsic Time ◽  
Time Scale Decomposition ◽  
Weak Fault ◽  
Levy Noise ◽  
The Impact

When early failures in rolling bearings occur, we need to be able to extract weak fault characteristic frequencies under the influence of strong noise and then perform fault diagnosis. Therefore, a new method is proposed: complete ensemble intrinsic time-scale decomposition with adaptive Lévy noise (CEITDALN). This method solves the problem of the traditional complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN) method not being able to filter nonwhite noise in measured vibration signal noise. Therefore, in the method proposed in this paper, a noise model in the form of parameter-adjusted noise is used to replace traditional white noise. We used an optimization algorithm to adaptively adjust the model parameters, reducing the impact of nonwhite noise on the feature frequency extraction. The experimental results for the simulation and vibration signals of rolling bearings showed that the CEITDALN method could extract weak fault features more effectively than traditional methods.

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