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We use orthogonality measures of Askey-Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey-Wilson polynomials are orthogonal martingale… (More)

We consider the tail behavior of random variables R which are solutions of the distributional equation R d = Q+MR, where (Q,M) is independent of R and |M | ≤ 1. Goldie and Grübel showed that the… (More)

We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a q-commutation relation.… (More)

- Jacek Wesolowski
- 1996

Problems of identification of a bivariate distribution of a random vector (X, Y) in terms of the conditional distribution YIX and the conditional mean E(XIY) have been intensively studied recently. A… (More)

- Agata Sakowicz, Jacek Wesolowski
- J. Multivariate Analysis
- 2014

AMS 2010 subject classifications: 62H05 62E10 39B22 Keywords: Neutrality with respect to partition Dirichlet distribution Method of moments Characterization a b s t r a c t Different concepts of… (More)

This paper is a continuation of our previous research on quadratic harnesses, i.e. processes with linear regressions and quadratic conditional variances. In this paper we define the class of… (More)

- Agnieszka Piliszek, Jacek Wesolowski
- J. Multivariate Analysis
- 2016

The paper develops a rather unexpected parallel to the multivariate Matsumoto--Yor (MY) property on trees considered in \cite{MW04}. The parallel concerns a multivariate version of the Kummer… (More)

We give an elementary construction of a time-invertible Markov process which is discrete except at one instance. The process is one of the quadratic harnesses studied in [5], [2], and [3]. It can be… (More)

- Jacek Wesolowski
- 2015

In this paper we study a Matsumoto-Yor type property for the gamma and Kummer inde- pendent variables discovered in Koudou and Vallois (2012). We prove that constancy of regressions of U = (1 + 1/(X… (More)

- Konstancja Bobecka, Pawel Hitczenko, Fernando López-Blázquez, Grzegorz Rempala, Jacek Wesolowski
- Combinatorics, Probability & Computing
- 2013

In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary)… (More)