scholarly journals Stochastic Monotonicity and Slepian-Type Inequalities for Infinitely Divisible and Stable Random Vectors

1993 ◽  
Vol 21 (1) ◽  
pp. 143-160 ◽  
Author(s):  
Gennady Samorodnitsky ◽  
Murad S. Taqqu
Keyword(s):  
Stochastic Monotonicity ◽  
Random Vectors ◽  
Infinitely Divisible ◽  
Stable Random Vectors

On dispersion of stable random vectors and its application in the prediction of multivariate stable processes

1994 ◽  
Vol 31 (3) ◽  
pp. 691-699 ◽  
Author(s):  
A. Reza Soltani ◽  
R. Moeanaddin
Keyword(s):  
Stable Process ◽  
Stable Processes ◽  
Random Vectors ◽  
Linear Predictor ◽  
Error Vector ◽  
Best Linear Predictor ◽  
Definition Of ◽  
Stable Random Vectors

Our aim in this article is to derive an expression for the best linear predictor of a multivariate symmetric α stable process based on many past values. For this purpose we introduce a definition of dispersion for symmetric α stable random vectors and choose the linear predictor which minimizes the dispersion of the error vector.

scholarly journals A formula for hidden regular variation behavior for symmetric stable distributions

Extremes ◽  
2020 ◽  
Vol 23 (4) ◽  
pp. 667-691
Author(s):  
Malin Palö Forsström ◽  
Jeffrey E. Steif
Keyword(s):  
Power Law ◽  
Spectral Measure ◽  
Regular Variation ◽  
Stable Distributions ◽  
Decay Rates ◽  
Random Vectors ◽  
Power Law Decay ◽  
Exact Power ◽  
Hidden Regular Variation ◽  
Stable Random Vectors

Abstract We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the corresponding spectral measure are needed to enter the set. One sees different decay rates in “different directions”, illustrating the phenomenon of hidden regular variation. We give several examples and obtain quite varied behavior, including sets which do not have exact power-law decay.

scholarly journals On Infinitely Divisible Random Vectors

1957 ◽  
Vol 28 (2) ◽  
pp. 461-470 ◽  
Author(s):  
Meyer Dwass ◽  
Henry Teicher
Keyword(s):  
Random Vectors ◽  
Infinitely Divisible

scholarly journals On regular variation for infinitely divisible random vectors and additive processes

2006 ◽  
Vol 38 (01) ◽  
pp. 134-148 ◽  
Author(s):  
Henrik Hult ◽  
Filip Lindskog
Keyword(s):  
Stochastic Processes ◽  
Regular Variation ◽  
Tail Behavior ◽  
Random Vectors ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Additive Process ◽  
Asymptotic Decay ◽  
Stationary Increments ◽  
Additive Processes

We study the tail behavior of regularly varying infinitely divisible random vectors and additive processes, i.e. stochastic processes with independent but not necessarily stationary increments. We show that the distribution of an infinitely divisible random vector is tail equivalent to its Lévy measure and we study the asymptotic decay of the probability for an additive process to hit sets far away from the origin. The results are extensions of known univariate results to the multivariate setting; we exemplify some of the difficulties that arise in the multivariate case.

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