The present book offers a detailed treatment of perturbed random walks, perpetuities, and
random processes with immigration. These objects are of major importance in modern …

We prove the existence and asymptotic behaviour of the transition density for a large class of
subordinators whose Laplace exponents satisfy lower scaling condition at infinity …

By a general shot noise process we mean a shot noise process in which the counting
process of shots is arbitrary locally finite. Assuming that the counting process of shots …

Abstract Let $(X_ {k},\xi _ {k}) _ {k\in\mathbb {N}} $ be a sequence of independent copies of
a pair $(X,\xi) $ where X is a random process with paths in the Skorokhod space $ D [0,\infty) …

We consider continuous-time Markov chains on integers which allow transitions to adjacent
states only, with alternating rates. This kind of processes are useful in the study of chain …

We prove a functional limit theorem for the number of visits by a planar random walk on
$\mathbb {Z}^ 2$ with zero mean and finite second moment to the points of a fixed finite set …

A. Weprove existence and asymptotic behavior of the transition density for a large class of
subordinators whose Laplace exponents satisfy lower scaling condition at infinity …

We define a general shot noise process as the convolution of a deterministic cadlag function
and a locally finite counting process concentrated on the nonnegative halfline. In this paper …

The weak convergence of centered shot noise processes to a stationary $\mathcal {L} _2 $-
process is proved under the assumption that the response function is mean square …

Od momentu charakteryzacji procesów Lévy'ego przez Paula Lévy'ego w latach 30. XX
wieku doczekały się one ogromnej liczby zastosowań w przeróżnych kontekstach. Między …