RECORD TIMES

ABSTRACT. Let X., X 2, ••■be independent and identically distributed random variables with a continuous distribution function. zL(zz) Ï ? is called a record time if X. . , is strictly larger than any previous X., and we put L(l)=l. The sequence 1 = L(l) < ¿(2) < L(3) < • • • of record times is a strictly increasing sequence of random variables. In the present note we investigate the sequence ÍL(zz)i through the ratios U(n)= L(n)/L(n — 1), zz > 2. We use an integer valued approximation T(zi) to U(n), defined as the smallest integer such that ü(n) < T(n). These approximations turn out to be independent and identically distributed. This fact makes it possible to deduce several limit laws for U(n) and for A(zz) = L(zz) — L(n — 1), zz > 2.