W. Mlotkowski

activity

20092022

most citedCauchy-Stieltjes families with polynomial variance functions and generalized orthogonality

17 citations · 62 across the 14 of their papers we have counts for

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9 papers · 1 filter

math.PR2021

Probability distributions with rational free $R$ -transform

Wojciech Młotkowski

We study the class $M_{ratio}$ of those probability distributions for which the free $R$ -transforms are rational functions. This class is closed under the additi…

math.PR2021

On freely quasi-infinitely divisible distributions

Ikkei Hotta, Wojciech Młotkowski, Noriyoshi Sakuma +1

Inspired by the notion of quasi-infinite divisibility (QID), we introduce and study the class of freely quasi-infinitely divisible (FQID) distributions on $R$ , i.e. distri…

math.PR2019★ 3 cited

Free self-decomposability and unimodality of the Fuss-Catalan distributions

Wojciech Młotkowski, Noriyoshi Sakuma, Yuki Ueda

We study properties of the Fuss-Catalan distributions $μ (p, r)$ , $p \geq 1$ , $0 < r \leq p$ : free infinite divisibility, free self-decomposability, free regularity and unimodality. We sh…

math.PR2017★ 17 cited

Cauchy-Stieltjes families with polynomial variance functions and generalized orthogonality

Wlodzimierz Bryc, Raouf Fakhfakh, Wojciech Mlotkowski

This paper studies variance functions of Cauchy-Stieltjes Kernel families generated by compactly supported centered probability measures. We describe several operations that allow…

math.PR2015

A family of sequences of binomial type

Wojciech Młotkowski, Anna Romanowicz

For delta operator $a D - b D^{p + 1}$ we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case $D - \frac{1}{2} D^{2}$ we show that the cor…

math.PR2015

A Fuss-type family of positive definite sequences

Wojciech Młotkowski, Karol A. Penson

We study a two-parameter family $a_{n} (p, t)$ of deformations of the Fuss numbers. We show a sufficient condition for positive definiteness of $a_{n} (p, t)$ and prove that some of the…

math.PR2013★ 3 cited

Probability distributions with binomial moments

Wojciech Mlotkowski, Karol A. Penson

We prove that if $p \geq 1$ and $- 1 \leq r \leq p - 1$ then the binomial sequence $(n n p + r)$ , $n = 0, 1, ...$ , is positive definite and is the moment sequence of a probability measur…

math.PR2013★ 3 cited

The probability measure corresponding to 2-plane trees

Wojciech Mlotkowski, Karol A. Penson

We study the probability measure $μ_{0}$ for which the moment sequence is $(n 3 n) \frac{1}{n + 1}$ . We prove that $μ_{0}$ is absolutely continuous, find the density function an…

math.PR2012

Densities of the Raney distributions

Wojciech Mlotkowski, Karol A. Penson, Karol Zyczkowski

We prove that if $p \geq 1$ and $0 < r \leq p$ then the sequence $(m m p + r) \frac{r}{m p + r}$ , $m = 0, 1, 2, ...$ , is positive definite, more precisely, is the moment sequence of a probab…