Limit theorems for the ratio of weak records

Let X1,X2,… be independent identically distributed (iid) random variables (rvs) with support on positive integers and (Wn,n⩾1) denote the corresponding sequence of weak record values. In the present paper we derive weak and strong limit theorems for the ratio of weak records Wn+m/Wn(n→∞). We also discuss the asymptotic behavior of a rv ξn which counts the number of weak record values that are equal to n.