in some long term studies, a series of dependent and possibly truncated life-times may be observed. suppose that the lifetimes have a common marginal distribution function. in left-truncation model, one observes data (xi,ti) only, when ti ≤ xi. under some regularity conditions, we provide a strong representation of the ßn estimator of ß = p(ti ≤ xi), in the form of an average of random variable...