Numbers of near bivariate record-concomitant observations

Let [email protected]?"1=(X"1,Y"1),[email protected]?"2=(X"2,Y"2),... be independent and identically distributed random vectors with continuous distribution. Let L(n) and X(n) denote the nth record time and the nth record value obtained from the sequence of Xs. Let Y(n) denote the concomitant of the nth record value, which relates to the sequence of Ys. We call [email protected]?"i a near bivariate nth record-concomitant observation if [email protected]?"i belongs to the open rectangle (X(n)-a,X(n))x(Y(n)-b"1,Y(n)+b"2), where a,b"1,b"2>0 and L(n)