Asymptotic Behavior of Conditional Laws and Moments of $\infty$-Stable Random Vectors, with Application to Upcrossing Intensities
Albin, J. M. P. ; Leadbetter, M. R.
Ann. Probab., Tome 27 (1999) no. 1, p. 1468-1500 / Harvested from Project Euclid
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We derive upper bounds for the conditional moment $\mathbf{E} \{| X|^{\varrho}|Y=y\}$ of a strictly $\alpha$-stable random vector (X,Y) when $\alpha\neq 1$ and $\varrho\leq 2$ and prove weak convergences for the conditional law $(X/u|Y= u)$ as $u \to \infty$ when $\alpha > 1$. As an example of application, we derive a new result in crossing theory for $\alpha$-stable processes.
Publié le : 1999-07-14
Classification:  Moment,  conditional moment,  conditional probability,  $\alpha$-stable distribution,  skewed $\alpha$-stable distribution,  crossing,  upcrossing,  upcrossing intensity,  60E07,  60F99,  62E20,  60G70,  60G99 
@article{1022677455,
     author = {Albin, J. M. P. and Leadbetter, M. R.},
     title = {Asymptotic Behavior of Conditional Laws and Moments of
		 $\infty$-Stable Random Vectors, with Application to Upcrossing
		 Intensities},
     journal = {Ann. Probab.},
     volume = {27},
     number = {1},
     year = {1999},
     pages = { 1468-1500},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1022677455}
}

Albin, J. M. P.; Leadbetter, M. R. Asymptotic Behavior of Conditional Laws and Moments of
		 $\infty$-Stable Random Vectors, with Application to Upcrossing
		 Intensities. Ann. Probab., Tome 27 (1999) no. 1, pp.  1468-1500. http://gdmltest.u-ga.fr/item/1022677455/