We characterize the subexponential densities on $(0,\infty)$ for compound Poisson distributions $[0,\infty)$ with absolutely continuous L\'evy measures. As a corollary, we show that class of all probability density functions $\mathbb R_+$ is closed under generalized convolution roots sums. Moreover, give an application to distribution supremum random walk.

We present a phenomenological model for the generation of human visual scanpaths. Successions of saccadic eye-movements are treated as realizations of a stochastic jump process in a random quenched salience eld. EEciency of the process is deened in terms of convergence properties of the time dependent probability of xating a region in the visual environment. Based on the assumption that the vis...

The spectral theory of random walks on networks arbitrary topology can be readily extended to study and L\'evy flights subject resetting these structures. When a discrete-time process is stochastically brought back from time its starting node, the mean search needed reach another node network may significantly decreased. In other cases, however, detrimental search. Using eigenvalues eigenvector...

We prove central limit theorems of Lindeberg-L evy and Lindeberg-Feller type for any K-invariant random variables on all irreducible symmetric spaces and irreducible symmetric cones, completing in this way the numerous partial results known before. In all cases the limit measures turn out to be Gaussian and being such a limit characterizes these measures. On the other hand we show that other cl...

? Abstract. This paper generalizes the Huet and L evy theory of normaliza-tion by neededness to an abstract setting. We deene Stable Deterministic Residual Structures (SDRS) and Deterministic Family Structures (DFS) by axiomatizing some properties of the residual relation and the family relation on redexes in an Abstract Rewriting System. We present two proofs of the Relative Normalization Theo...

We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble times-series, generated experimentally or numerically, without having knowledge about exact underlying dynamics. The reasons diffusive scaling mean-squared displacement are decomposed into three root causes: increment correlations expressed by "Joseph effect" [Mandelbrot 1968], fat-tails proba...

We derive formulas for the moments of ruin time in a L\'evy risk model and use these to determine asymptotic behavior as initial capital tends infinity. In special case perturbed Cram\'er-Lundberg with phase-type or exponentially distributed claims, we explicitly compute first two time. All our considerations distinguish between profitable unprofitable setting.

We establish two precise asymptotic results on the Birkhoff sums for dynamical systems. These are parallel to that arithmetic of independent and identically distributed random variables previously obtained by Hsu Robbins, Erd\H{o}s, Heyde. apply our Gauss map obtain new asymptotics in theorem L\'evy regular continued fraction expansion irrational numbers $(0,1)$.

The in nitely divisible distributions on R+ of random variables Ct, St and Tt with Laplace transforms 1 cosh p 2 t ; p 2 sinh p 2 !t ; and tanh p 2 p 2 !t respectively are characterized for various t > 0 in a number of di erent ways: by simple relations between their moments and cumulants, by corresponding relations between the distributions and their L evy measures, by recursions for their Mel...