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13 papers · 2 filters
An Erdös-Révész type law of the iterated logarithm for reflected fractional Brownian motion
K. Dębicki, K. M. Kosiński
Let be a fractional Brownian motion with Hurst parameter . For the stationary storage process $Q_{B_H}(t)=\sup_{-\infty<s\le t}(B_H(t)-B_H…
Oscillating heat kernels on ultrametric spaces
Alexander Bendikov, Wojciech Cygan, Wolfgang Woess
Let be a proper ultrametric space. Given a measure on and a function defined on the collection of all non-singleton balls of , we consider t…
Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes
Viktor Bezborodov, Luca Di Persio, Tyll Krueger +2
We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth mo…
A note on ruin problems in perturbed classical risk models
Peng Liu, Chunsheng Zhang, Lanpeng Ji
In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing…
Uniform tail approximation of homogenous functionals of Gaussian fields
Krzysztof Dȩbicki, Enkelejd Hashorva, Peng Liu
Let be a centered Gaussian random field with continuous trajectories and set with some positive function. Classical results establis…
Asymptotic behaviour and estimates of slowly varying convolution semigroups
Tomasz Grzywny, Michał Ryznar, Bartosz Trojan
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on under the assumption that its…