Ignatov's theorem and correlated record values

For a sequence of i.i.d. random variables an upper (lower) k-record is a value which is kth largest (smallest) at its appearance. A consequence of Ignatov's theorem is that the event a value x ever appears as an upper k-record is independent of the event a value y ever appears as an upper j-record, when either j[not equal to]k or x[not equal to]y. We study the correlation between the event a value ever appears as an upper k-record and the event a value ever appears as a lower j-record, and show that it can be strictly positive or negative depending on simple criteria. We also show that these events are, as either j or k increases, asymptotically independent.