scholarly journals On limiting cluster size distributions for processes of exceedances for stationary sequences

2010 ◽  
Vol 80 (23-24) ◽  
pp. 1814-1818 ◽  
Author(s):  
Konstantin Borovkov ◽  
Serguei Novak
Keyword(s):  
Cluster Size ◽  
Size Distributions ◽  
Stationary Sequences

scholarly journals The upcrossings index and the extremal index

2006 ◽  
Vol 43 (4) ◽  
pp. 927-937 ◽  
Author(s):  
H. Ferreira
Keyword(s):  
Point Process ◽  
Cluster Size ◽  
Extremal Index ◽  
Size Distributions ◽  
Mixing Conditions ◽  
Stationary Sequences ◽  
New Family ◽  
Local Restriction

For stationary sequences X = {Xn}n≥1 we relate τ, the limiting mean number of exceedances of high levels un by X1,…,Xn, and ν, the limiting mean number of upcrossings of the same level, through the expression θ = (ν/τ)η, where θ is the extremal index of X and η is a new parameter here called the upcrossings index. The upcrossings index is a measure of the clustering of upcrossings of u by variables in X, and the above relation extends the known relation θ = ν/τ, which holds under the mild-oscillation local restriction D″(u) on X. We present a new family of local mixing conditions D̃(k)(u) under which we prove that (a) the intensity of the limiting point process of upcrossings and η can both be computed from the k-variate distributions of X; and (b) the cluster size distributions for the exceedances are asymptotically equivalent to those for the lengths of one run of exceedances or the lengths of several consecutive runs which are separated by at most k − 2 nonexceedances and, except for the last one, each contain at most k − 2 exceedances.

scholarly journals The upcrossings index and the extremal index

2006 ◽  
Vol 43 (04) ◽  
pp. 927-937 ◽  
Author(s):  
H. Ferreira
Keyword(s):  
Point Process ◽  
Cluster Size ◽  
Extremal Index ◽  
Size Distributions ◽  
Mixing Conditions ◽  
Stationary Sequences ◽  
New Family ◽  
Local Restriction

For stationary sequences X = {X n } n≥1 we relate τ, the limiting mean number of exceedances of high levels u n by X 1,…,X n , and ν, the limiting mean number of upcrossings of the same level, through the expression θ = (ν/τ)η, where θ is the extremal index of X and η is a new parameter here called the upcrossings index. The upcrossings index is a measure of the clustering of upcrossings of u by variables in X , and the above relation extends the known relation θ = ν/τ, which holds under the mild-oscillation local restriction D″( u ) on X . We present a new family of local mixing conditions D̃ (k)( u ) under which we prove that (a) the intensity of the limiting point process of upcrossings and η can both be computed from the k-variate distributions of X ; and (b) the cluster size distributions for the exceedances are asymptotically equivalent to those for the lengths of one run of exceedances or the lengths of several consecutive runs which are separated by at most k − 2 nonexceedances and, except for the last one, each contain at most k − 2 exceedances.

Infrared laser action on the spatial, velocity, and cluster-size distributions in an SF6 free jet

1984 ◽  
Vol 84 (3) ◽  
pp. 345-358 ◽  
Author(s):  
P. Melinon ◽  
R. Monot ◽  
J.-M. Zellweger ◽  
H. van den Bergh
Keyword(s):  
Cluster Size ◽  
Laser Action ◽  
Infrared Laser ◽  
Size Distributions ◽  
Free Jet ◽  
Spatial Velocity

Experimental equivalent cluster-size distributions in nanometric volumes of liquid water

2004 ◽  
Vol 110 (1-4) ◽  
pp. 851-857 ◽  
Author(s):  
B. Grosswendt ◽  
L. De Nardo ◽  
P. Colautti ◽  
S. Pszona ◽  
V. Conte ◽  
...  
Keyword(s):  
Liquid Water ◽  
Cluster Size ◽  
Size Distributions

Metal cluster size distributions during nozzle jet expansion

1986 ◽  
Vol 48 (17) ◽  
pp. 1122-1124 ◽  
Author(s):  
S.‐N. Yang ◽  
T.‐M. Lu
Keyword(s):  
Cluster Size ◽  
Metal Cluster ◽  
Size Distributions

scholarly journals Large deviations for cluster size distributions in a continuous classical many-body system

2015 ◽  
Vol 25 (2) ◽  
pp. 930-973 ◽  
Author(s):  
Sabine Jansen ◽  
Wolfgang König ◽  
Bernd Metzger
Keyword(s):  
Large Deviations ◽  
Cluster Size ◽  
Size Distributions ◽  
Body System ◽  
Many Body
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