Abstract
We consider a sequence (X-i,Y-j)(1 <= j <= n) of independent and identically distributed randomvariables with joint cumulative distribution H(x,y), which has exponential marginals F(x) and G(y) with parameter lambda= 1. We also assume that X-i(omega) not equal Y-i(omega), for all i subset of N, and omega is an element of Omega. We denote {R-k((j))}(k >= 1) and {S-k((j))..}(k >= 1) by the sequences of the.. th records in the sequences (X-i)(1 <= j <= n) , (Y-j)(1 <= j <= n) , respectively. The main result of of the paper is to prove the asymptotic independence of {R-k((j))}(k >= 1) and {S-k((j))..}(k >= 1)using the property of stopping time of the jth record times and that of the exponential distribution.