6 problems

Let $\alpha,\beta\in(0,1]$, and let $X_{\alpha}$ and $X_{\beta}$ be independent Mittag-Leffler random variables with power indices $\alpha$ and $\beta$, respectively, and equal tim…

Let $(X_k)$ be independent copies of a nondegenerate nonnegative random variable, let $S_n=X_1+\cdots+X_n$, and set $Z_n=\sum_{k=1}^n e^{\imath S_k}$. For $p>0$, write…

Let $\tau$ and $\hat\tau$ be renewal sets with tail exponents … , respectively, and let $h_c(\beta)$ and $h_c^a(\beta)$ denote the quenched and annealed critical points of the pinn…

Let $C_k^{1,1}$ be the renewal-sequence random variable whose point probabilities are under consideration, and let $\zeta(j)$ denote the Riemann zeta function. For each $k\geq 1$ a…

Let $\nu$ be a probability measure on $\mathbb R$ with finite mean $m<\infty$, and let $Q_\nu$ be the stationary renewal process on $\mathbb R$ with renewal distribution $\nu$. A w…

Let a cyclic polling system have general renewal arrival processes and deterministic switch-over times. The system is considered in the regime where the deterministic switch-over t…