RECORDS AND 2-BLOCK RECORDS OF 1-DEPENDENT STATIONARY-SEQUENCES UNDERLOCAL DEPENDENCE

We first study the records of several examples of 1-dependent stationa ry sequences {X-n}, some of them which satisfy a local independence co ndition introduced in Haiman (1987a), whereas the other do not satisfy this condition. For the second category (called with local dependence ), we then extend a result of the above cited paper by proving, (under some regularity conditions on the joint distribution of (X-1, X-2, X- 3)), that the 2-block record times of {X-n} a.s. coincide, (via a tran slation of the time index and from some index on) with the record time s of an appropriately constructed i.i.d. sequence {(X) over cap(n)}, w hereas the 2-block record values of {X-n} and the record values of {(X ) over cap(n)} are imbricate. (C) Elsevier, Paris.