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On the exponential Orlicz norms of stopped Brownian motion

Goran Peškir (1996)

Studia Mathematica

Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by ψ p ( x ) = e x p ( | x | p ) - 1 with 0 < p ≤ 2) of m a x 0 t τ | B t | or | B τ | to be finite, where B = ( B t ) t 0 is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that m a x 0 t τ | B t | ψ 1 < as soon as E ( τ k ) = O ( C k k k ) for some constant C > 0 as k → ∞ (or equivalently τ ψ 1 < ). In particular, if τ ∼ Exp(λ) or | N ( 0 , σ 2 ) | then the last condition is satisfied, and we obtain m a x 0 t τ | B t | ψ 1 K E ( τ ) with some universal constant K > 0....

On the Extinction Probability for Bisexual Branching Processes in Varying Environments

Molina, Manuel, Mota, Manuel, Ramos, Alfonso (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 60J80In this paper, the bisexual branching process in varying environments introduced in [9] is considered and some sufficient conditions for the existence of positive probability of non-extinction are established.Research supported by the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grant BFM2000-0356 and the Consejería de Educación, Ciencia y Tecnología de la Junta de Extremadura and the Fondo Social Europeo, grant IPR00A056....

On the extremal behavior of a Pareto process: an alternative for ARMAX modeling

Marta Ferreira (2012)

Kybernetika

In what concerns extreme values modeling, heavy tailed autoregressive processes defined with the minimum or maximum operator have proved to be good alternatives to classical linear ARMA with heavy tailed marginals (Davis and Resnick [8], Ferreira and Canto e Castro [13]). In this paper we present a complete characterization of the tail behavior of the autoregressive Pareto process known as Yeh-Arnold-Robertson Pareto(III) (Yeh et al. [32]). We shall see that it is quite similar to the first order...

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