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On the divergence of certain integrals of the Wiener process

Lawrence A. Shepp, John R. Klauder, Hiroshi Ezawa (1974)

Annales de l'institut Fourier

Let f ( x ) be a nonnegative function with its only singularity at x = 0 , e.g. f ( x ) = | x | - α , α > 0 . We study the behavior of the Wiener process W ( t ) in left and right hand neighborhoods of level crossings by finding necessary and sufficient conditions on f for the integrals of f ( W ( t ) ) to be finite or infinite.

On the equivalence of some eternal additive coalescents

Anne-Laure Basdevant (2008)

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we study additive coalescents. Using their representation as fragmentation processes, we prove that the law of a large class of eternal additive coalescents is absolutely continuous with respect to the law of the standard additive coalescent on any bounded time interval.

On the exchanges between Wolfgang Doeblin and Bohuslav Hostinský

Laurent Mazliak (2007)

Revue d'histoire des mathématiques

We present the letters sent by Wolfgang Doeblin to Bohuslav Hostinský between 1936 and 1938. They concern some aspects of the general theory of Markov chains and the solutions of the Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis.

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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