On the continuous dual Hahn process. (English) Zbl 1483.60107
The author extends the continuous dual Hahn process \((\mathbb{T}_t)\) of I. Corwin and A. Knizel [“Stationary measure for the open KPZ equation”, Preprint, arXiv:2103.12253] from a finite time interval to the entire real line by taking a limit of a closely related Markov process \((T_t).\) The processes \((T_t) \) are characterized by conditional means and variances under bidirectional conditioning, and it is proved that continuous dual Hahn polynomials are orthogonal martingale polynomials for both processes.
Reviewer: Nasir N. Ganikhodjaev (Tashkent)
MSC:
| 60J25 | Continuous-time Markov processes on general state spaces |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
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