Bilateral Birth and death process in quantum calculus
Abstract
In this paper I shall give the complete solution of the equations governing the bilateral birth and death process on path set $\mathbb{R}_q=\{q^n,\quad n\in\mathbb{Z}\}$ in which the birth and death rates $\lambda_n=q^{2\nu-2n}$ and $\mu_n=q^{-2n}$ where $0<q<1$ and $\nu>-1$ . The mathematical methods employed here are based on $q$-Bessel Fourier analysis.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.14283
- arXiv:
- arXiv:2106.14283
- Bibcode:
- 2021arXiv210614283D
- Keywords:
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- Mathematics - Probability