Bi-Poisson process

Abstract

We study a two parameter family of processes with linear regressions and linear conditional variances. We give conditions for the unique solution of this problem, and point out the connection between the resulting Markov processes and the generalized convolutions introduced by Bożejko and Speicher.

12 pages, 2 figures

References in corpus (2)

• On a class of free Levy laws related to a regression problem
• Conditional moments of q-Meixner processes

Cited by in corpus (11)

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• Expansions of one density via polynomials orthogonal with respect to the other
• On the structure and probabilistic interpretation of Askey-Wilson densities and polynomials with complex parameters
• Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses
• The bi-Poisson process: a quadratic harness
• $q-$Wiener ($\alpha ,q)-$ Ornstein-Uhlenbeck processes. A generalization of known processes
• Befriending Askey-Wilson polynomials
• A few remarks on quadratic harnesses
• Semigroups of distributions with linear Jacobi parameters
• Markov processes, polynomial martingales and orthogonal polynomials
• Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths