Let (Ut,Vt) be a bivariate Lévy process, where Vt is a subordinator and Ut is a Lévy process formed by randomly weighting each jump of Vt by an independent random variable Xt having cdf F. We investigate the asymptotic distribution of the self-normalized Lévy process Ut/Vt at 0 and at ∞. We...

Let Ξ0=[−1,1], and define the segments Ξn recursively in the following manner: for every n=0,1,…, let Ξn+1=Ξn∩[an+1−1,an+1+1], where the point an+1 is chosen randomly on the segment Ξn with uniform distribution. For the radius ρn of Ξn, we prove that n(ρn−1/2) converges in...

The paradoxical results of Csörgo and Simons for mutually beneficial sharing among any fixed number of St. Petersburg gamblers are extended to games played by a possibly biased coin, with p as the probability of 'heads.' The extension is not straightforward because, unlike in the classical case...