Corrigendum to “Large Deviations for Generalized Polya urns with arbitrary Urn Function” [Stochastic Processes and their Applications 127 (2017) 3372 – 3411]

Abstract

We find and correct a mistake in the formulas for the cumulant generating function $\psi$ of the linear urn problem that are given in the Corollary 12 of Franchini (2017), and its proof. In particular, the correct function ${\psi }_{+}$ is as follows: $e^{-{\psi }_{+}\left(\lambda ;b>0\right)}=1-\frac{a}{b}{e}^{\frac{a}{b}\lambda }{\left(1-e^{-\lambda }\right)}^{\frac{1}{b}}B\left(\frac{a}{b},\frac{b-1}{b};1-e^{-\lambda },1\right)$for the positive branch $b>0$ and $e^{-{\psi }_{+}\left(\lambda ;b<0\right)}=1+\frac{a}{b}{e}^{\frac{a}{b}\lambda }{\left(1-e^{-\lambda }\right)}^{\frac{1}{b}}B\left(\frac{a}{b},\frac{b-1}{b};0,1-e^{-\lambda }\right)$for the negative branch $b<0$. We remark that this issue does not affect the main result, nor any other finding of the paper. We also correct a minor typo in the proof of Theorem 9.