scholarly journals Ergodic theory, Abelian groups and point processes induced by stable random fields

2010 ◽  
Vol 38 (2) ◽  
pp. 770-793 ◽  
Author(s):  
Parthanil Roy
Keyword(s):  
Ergodic Theory ◽  
Random Fields ◽  
Point Processes ◽  
Abelian Groups ◽  
Stable Random Fields

A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular ℤd-actions

2018 ◽  
Vol 55 (1) ◽  
pp. 179-195
Author(s):  
Ayan Bhattacharya ◽  
Parthanil Roy
Keyword(s):  
Random Field ◽  
Sample Size ◽  
Power Function ◽  
Ergodic Theory ◽  
Random Fields ◽  
Large Sample ◽  
Discrete Parameter ◽  
Sample Test ◽  
Block Maxima ◽  
Stable Random Fields

AbstractBased on the ratio of two block maxima, we propose a large sample test for the length of memory of a stationary symmetric α-stable discrete parameter random field. We show that the power function converges to 1 as the sample-size increases to ∞ under various classes of alternatives having longer memory in the sense of Samorodnitsky (2004). Ergodic theory of nonsingular ℤd-actions plays a very important role in the design and analysis of our large sample test.

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

scholarly journals Operator scaling stable random fields

2007 ◽  
Vol 117 (3) ◽  
pp. 312-332 ◽  
Author(s):  
Hermine Biermé ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Fields ◽  
Stable Random Fields

scholarly journals Extrapolation of stable random fields

2013 ◽  
Vol 115 ◽  
pp. 516-536 ◽  
Author(s):  
Wolfgang Karcher ◽  
Elena Shmileva ◽  
Evgeny Spodarev
Keyword(s):  
Random Fields ◽  
Stable Random Fields

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (03) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

Sign in / Sign up

Export Citation Format

Share Document