Nonstationary space–time covariance functions induced by dynamical systems

2021 ◽  
Author(s):  
Rachid Senoussi ◽  
Emilio Porcu
Keyword(s):  
Dynamical Systems ◽  
Space Time ◽  
Covariance Functions

Computational Analysis of the U.S. Forest Fires

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
António M. Lopes ◽  
J. A. Tenreiro Machado
Keyword(s):  
Dynamical Systems ◽  
Forest Fires ◽  
Computational Analysis ◽  
Space Time ◽  
Burn Severity ◽  
Computational Visualization ◽  
The U.S

This paper analyses forest fires (FF) in the U.S. during 1984–2013, based on data collected by the monitoring trends in burn severity (MTBS) project. The study adopts the tools of dynamical systems to tackle information about space, time, and size. Computational visualization methods are used for reducing the information dimensionality and to unveil the relationships embedded in the data.

A Nonparametric Assessment of Properties of Space–Time Covariance Functions

2007 ◽  
Vol 102 (478) ◽  
pp. 736-744 ◽  
Author(s):  
Bo LI ◽  
Marc G Genton ◽  
Michael Sherman
Keyword(s):  
Space Time ◽  
Covariance Functions

scholarly journals Simulating space-time random fields with nonseparable Gneiting-type covariance functions

2020 ◽  
Vol 30 (5) ◽  
pp. 1479-1495
Author(s):  
Denis Allard ◽  
Xavier Emery ◽  
Céline Lacaux ◽  
Christian Lantuéjoul
Keyword(s):  
Random Fields ◽  
Space Time ◽  
Covariance Functions

scholarly journals Space-time models based on random fields with local interactions

2016 ◽  
Vol 30 (15) ◽  
pp. 1541007 ◽  
Author(s):  
Dionissios T. Hristopulos ◽  
Ivi C. Tsantili
Keyword(s):  
Langevin Equation ◽  
Equations Of Motion ◽  
Real Life ◽  
Stochastic Perturbation ◽  
Space Time ◽  
Gaussian Field ◽  
Time Data ◽  
Time Dynamics ◽  
Covariance Functions ◽  
Curvature Term

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

Sign in / Sign up

Export Citation Format

Share Document