Jolanta Misiewicz
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View article: How Exceptional is the Extremal Kendall and Kendall-Type Convolution
How Exceptional is the Extremal Kendall and Kendall-Type Convolution Open
This paper deals with the generalized convolutions connected with the Williamson transform and the maximum operation. We focus on such convolutions which can define transition probabilities of renewal processes. They should be monotonic si…
View article: On Weak Generalized Stability of Random Variables via Functional Equations
On Weak Generalized Stability of Random Variables via Functional Equations Open
In this paper we characterize random variables which are stable but not strictly stable in the sense of generalized convolution. We generalize the results obtained in Jarczyk and Misiewicz (J Theoret Probab 22:482-505, 2009), Misiewicz and…
View article: Cramér–Lundberg model for some classes of extremal Markov sequences
Cramér–Lundberg model for some classes of extremal Markov sequences Open
The classical Cramér–Lundberg model was the first attempt to describe the financial condition of the insurance company. The incomes were approximated by a steady stream of money, and insurance payments were not limited and could take any v…
View article: Band copulas as spectral measures for two-dimensional stable random vectors
Band copulas as spectral measures for two-dimensional stable random vectors Open
In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.
View article: About the density of spectral measure of the two-dimensional SaS random vector
About the density of spectral measure of the two-dimensional SaS random vector Open
In this paper, we consider a symmetric α-stable p-sub-stable twodimensional random vector.Our purpose is to show when the function exp -(|a| p + |b| p ) α/p is a characteristic function of such a vector for some p and α.The solution of thi…
View article: How exceptional is the extremal Kendall and Kendall-type convolution
How exceptional is the extremal Kendall and Kendall-type convolution Open
This paper deals with the generalized convolutions connected with the Williamson transform and the maximum operation. We focus on such convolutions which can define transition probabilities of renewal processes. They should be monotonic si…
View article: Every symmetric weakly-stable random vector is pseudo-isotropic
Every symmetric weakly-stable random vector is pseudo-isotropic Open
In 1938, Schoenberg [20] posed a few seemingly simple problems in the area of elementary probability theory. The main goal was to characterize all the pseudo-isotropic distributions; that is, probability distributions in which all the one-…
View article: Cramer-Lundberg model for some classes of extremal Markov sequences
Cramer-Lundberg model for some classes of extremal Markov sequences Open
The classical Cramer-Lundberg model was the first attempt to describe the financial condition of the insurance company. The incomes were approximated by a steady stream of money, insurance payments were not limited and could take any value…
View article: Generalized convolutions and the Levi-Civita functional equation
Generalized convolutions and the Levi-Civita functional equation Open
In Borowiecka et al. (Bernoulli 21(4):2513–2551, 2015) the authors show that every generalized convolution can be used to define a Markov process, which can be treated as a Lévy process in the sense of this convolution. The Bessel process …
View article: Renewal theory for extremal Markov sequences of the Kendall type
Renewal theory for extremal Markov sequences of the Kendall type Open
The paper deals with renewal theory for a class of extremal Markov sequences connected with the Kendall convolution. We consider here some particular cases of the Wold processes associated with generalized convolutions. We prove an analogu…
View article: Lévy processes and stochastic integrals in the sense of generalized convolutions
Lévy processes and stochastic integrals in the sense of generalized convolutions Open
In this paper, we present a comprehensive theory of generalized and weak\ngeneralized convolutions, illustrate it by a large number of examples, and\ndiscuss the related infinitely divisible distributions. We consider L\\'{e}vy\nand additi…
View article: Kendall random walk, Williamson transform and the corresponding Wiener-Hopf factorization
Kendall random walk, Williamson transform and the corresponding Wiener-Hopf factorization Open
The paper gives some properties of hitting times and an analogue of the Wiener-Hopf factorization for the Kendall random walk. We show also that the Williamson transform is the best tool for problems connected with the Kendall generalized …