Wojciech Matysiak
Warsaw University of Technology
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Publication
Featured researches published by Wojciech Matysiak.
Transactions of the American Mathematical Society | 2007
Wlodzimierz Bryc; Wojciech Matysiak; Jacek Wesołowski
We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a -commutation relation. This implies that quadratic harnesses are essentially determined uniquely by five numerical constants. Explicit recurrences for the orthogonal martingale polynomials are derived in several cases of interest.
arXiv: Classical Analysis and ODEs | 2005
Wlodzimierz Bryc; Wojciech Matysiak; Paweł J. Szabłowski
We solve the connection coefficient problem between the Al-Salam-Chihara polynomials and the q-Hermite polynomials, and we use the resulting identity to answer a question from probability theory. We also derive the distribution of some Al-Salam-Chihara polynomials, and compute determinants of related Hankel matrices.
Annals of Probability | 2008
Wlodzimierz Bryc; Wojciech Matysiak; Jacek Wesołowski
This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam-Chihara polynomials and a relation between these polynomials for different values of parameters.
Infinite Dimensional Analysis, Quantum Probability and Related Topics | 2011
Krzysztof Drożdżewicz; Wojciech Matysiak
A method for computing the mixed moments of (not necessarily commutative) random vectors from the first order moments, the
Medical Science Monitor | 2006
Agnieszka Jezierska; Wojciech Matysiak; Tomasz Motyl
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Medical Science Monitor | 2006
Agnieszka Jezierska; Wojciech P. Olszewski; Jerzy Pietruszkiewicz; Włodzimierz T. Olszewski; Wojciech Matysiak; Tomasz Motyl
-commutators between the annihilation and creation operators, and the
Annals of Probability | 2002
Wojciech Matysiak; Paweł J. Szabłowski
q
Stochastic Processes and their Applications | 2011
Wlodzimierz Bryc; Wojciech Matysiak; Jacek Wesołowski
-commutators between the annihilation and preservation operators, is presented. The method is illustrated by a relevant characterization of
Stochastic Processes and their Applications | 2015
Wojciech Matysiak; Marcin Świeca
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arXiv: Probability | 2005
Wojciech Matysiak; Paweł J. Szabłowski
-Gaussian vectors.
