• Corpus ID: 248863208

Fluctuations of extremal Markov chains driven by the Kendall convolution

  title={Fluctuations of extremal Markov chains driven by the Kendall convolution},
  author={Barbara H. Jasiulis-Gołdyn and Edward Omey and Mateusz Staniak},
. The paper deals with fluctuations of Kendall random walks, which are extremal Markov chains and iterated integral transforms with the Williamson kernel Ψ( t ) = (1 − | t | α ) + , α > 0. We obtain the joint distribution of the first ascending ladder epoch and height over any level a 0 and distribution of maximum and minimum for these extremal Markovian sequences solving recursive integral equations. We show that distribution of the first crossing time of level a 0 is a mixture of geometric and… 



Kendall random walks

The paper deals with a new class of random walks strictly connected with the Pareto distribution. We consider stochastic processes in the sense of generalized convolution or weak generalized

Renewal theory for extremal Markov sequences of Kendall type

Introductory Lectures on Fluctuations of Lévy Processes with Applications

Levy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance

An extremal markovian sequence

In this paper we consider an independent and identically distributed sequence {Yn } with common distribution function F(x) and a random variable X 0, independent of the Yi 's, and define a Markovian

Lévy processes and stochastic integrals in the sense of generalized convolutions

In this paper, we present a comprehensive theory of generalized and weak generalized convolutions, illustrate it by a large number of examples, and discuss the related infinitely divisible

The Urbanik generalized convolutions in the non-commutative probability and a forgotten method of constructing generalized convolution

The paper deals with the notions of weak stability and weak generalized convolution with respect to a generalized convolution, introduced by Kucharczak and Urbanik. We study properties of such

Kendall random walk,Williamson transform, and the corresponding Wiener–Hopf factorization

We give some properties of hitting times and an analogue of the Wiener–Hopf factorization for the Kendall random walk. We also show that the Williamson transform is the best tool for problems

Classical definitions of the Poisson process do not coincide in the case of generalized convolutions

In the paper, we consider a generalization of the notion of Poisson process to the case where the classical convolution is replaced by the generalized convolution in the sense of Urbanik [K. Urbanik,

L\'evy processes with respect to the index Whittaker convolution

The index Whittaker convolution operator, recently introduced by the authors, gives rise to a convolution measure algebra having the property that the convolution of probability measures is a

Joint distribution of the first hitting time and first hitting place for a random walk

A random walk on the real line starting from 0 is considered. A representation of the Lapalace-Founer transform of the joint distribution of the first hitting time and the first hitting place of the