Conditional moments of q-Meixner processes

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 Levy processes.

LaTeX, 24 pages. Corrections to published version affect formulas in Theorem 4.2

References in corpus (2)

• Free martingale polynomials
• Spectra of Hamiltonians with Generalized Single-Site Dynamical Disorder

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• Dual Lukacs regressions of negative orders for non-commutative variables
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• Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths