Conditional moments of q-Meixner processes
By Wlodzimierz Bryc, J. Wesołowski. 2004
68 citations recorded by the source corpus.
Abstract.We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-parameter family of orthogonal polynomials which generalize the Meixner polynomials. Special cases of these processes are known to arise from the non-commutative generalizations of the Lévy processes.
Subfields: Applied Mathematics, Management Information Systems, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/63660037b98a17cda9cc9a47164e6884933d0563
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In Applied Mathematics
In Management Information Systems
In Statistics and Probability
Citations in the corpus
- On a class of free Lévy laws related to a regression problem (2004, methodology): “ case q = 1 and the free case q = 0. The interpolating q-deformed Meixner laws appear also as the laws of classical stochastic processes with linear regressions and quadratic conditional variances in [16]. To facilitate the comparison with the latter paper, in this note we parameterize the free Meix”
- Askey--Wilson polynomials, quadratic harnesses and martingales (2008, background): “(Zt|Fs,u)= u−t u−s Zs + t−s u−s (2.23) Zu and Var(Zt|Fs,u)= (u−t)(t−s) u−qs 1−(1−q) (uZs −sZu)(Zu −Zs) (u−s)2 (2.24) , 14 W. BRYC AND J. WESOL OWSKI which correspond to the q-Brownian motion (see [10], Theorem 4.1). Here, (Zt) is defined only on a possibly-bounded time domain I(A,B,C,D), and the co”