Let Y0,Y1,Y2,... be an i.i.d. sequence of random variables with absolutely continuous distribution function F, and let {N(t),t≥0} be a Poisson process with rate λ(t) and mean ℝ(t), independent of the Yj’s. The authors associate Y0 with the point t=0, and Yj with the jth point of N(ë), j≥1. The first Yj(j≥1) to exceed all previous ones is the first record value, and the time of its occurrence is the first record time; subsequent record values and times are defined analogously. For general ℝ, the authors give the joint distribution of the values and times of the first n records to occur after a fixed time T, 0•T<•. Assuming that F satisfies Von Mises regularity conditions, and that λ(t)/ℝ(t)⇒c∈(0,•) as t⇒•, they find the limiting joint p.d.f. of the values and times of the first n records after T, as T⇒•. In the course of this the authors correct a result of Gaver and Jacobs. They also consider limiting marginal and conditional distributions. In addition, the authors extend a known result for the limit as the number of records K⇒•, and they compare the results for the limit as T⇒• with those for the limit as K⇒•.
