A new approach for simulation of non-Gaussian processes

2013 ◽  
Vol 166 (9) ◽  
pp. 482-493
Author(s):  
Jing Li ◽  
Xin Wang
Keyword(s):  
Gaussian Processes ◽  
New Approach ◽  
Non Gaussian

scholarly journals Structure factors for generalized grey Browinian motion

2019 ◽  
Vol 22 (2) ◽  
pp. 396-411
Author(s):  
José L. da Silva ◽  
Ludwig Streit
Keyword(s):  
Gaussian Processes ◽  
Form Factors ◽  
Analytic Form ◽  
Debye Function ◽  
Asymptotic Decay ◽  
Structure Factors ◽  
Closed Analytic Form ◽  
Non Gaussian

Abstract In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.

scholarly journals Gaussian and non-Gaussian processes of zero power variation

2015 ◽  
Vol 19 ◽  
pp. 414-439 ◽  
Author(s):  
Francesco Russo ◽  
Frederi Viens
Keyword(s):  
Gaussian Processes ◽  
Power Variation ◽  
Non Gaussian

scholarly journals Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory

Atmosphere ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 248
Author(s):  
Nan Chen ◽  
Xiao Hou ◽  
Qin Li ◽  
Yingda Li
Keyword(s):  
Information Theory ◽  
Dynamical Systems ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Model Error ◽  
High Dimensions ◽  
New Approach ◽  
Fluctuation Dissipation ◽  
Spectrum Density ◽  
Non Gaussian

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Quantifying the model error and model uncertainty plays an important role in understanding and predicting complex dynamical systems. In the first part of this article, a simple information criterion is developed to assess the model error in imperfect models. This effective information criterion takes into account the information in both the equilibrium statistics and the temporal autocorrelation function, where the latter is written in the form of the spectrum density that permits the quantification via information theory. This information criterion facilitates the study of model reduction, stochastic parameterizations, and intermittent events. In the second part of this article, a new efficient method is developed to improve the computation of the linear response via the Fluctuation Dissipation Theorem (FDT). This new approach makes use of a Gaussian Mixture (GM) to describe the unperturbed probability density function in high dimensions and avoids utilizing Gaussian approximations in computing the statistical response, as is widely used in the quasi-Gaussian (qG) FDT. Testing examples show that this GM FDT outperforms qG FDT in various strong non-Gaussian regimes.

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