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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 6-7: Proceedings of the Hammamet Conference, 19-23 October 2015
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Articles

Jacobi sequences of squares of random variables

, &
Pages 868-882 | Received 03 Oct 2016, Accepted 07 Oct 2016, Published online: 03 Nov 2016
 

Abstract

We express the Jacobi sequences of the square of a real valued random variable with all moments, not necessarily symmetric, as functions of the corresponding sequences of the random variable itself. In the symmetric case, the result is known and, we give a short, purely algebraic proof of it. We apply our result to the square of the Gamma distribution, i.e. the 4th power of the standard Gaussian. The result confirms the conjecture that belongs to the polynomial class, but its principal Jacobi sequence grows like , not as expected.

Acknowledgements

LA acknowledges support by the Russian Science Foundation N. RSF 14-11-00687, Steklov Mathematical Institute.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Russian Science Foundation N. [RSF 14-11-00687], Steklov Mathematical Institute.

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