Bivariate lower bounds given by Galainbos and Xu (1993) and Lee (1992) are generalized. Examples cast light on the problem of the structure and optimality of the bounds.

A proof is given of the basic normed-convergence theorem for the ordinary supercritical Bienaymé-Galton-Watson process with finite mean. Part of it is adapted to obtain an analogous result for inhomogeneous supercritical processes (i.e. branching processes in varying environment). This is used...

A limit theorem is developed for sample partial autocorrelations, when the vector {N1/2(R(k)-mk), K=1,...,H} converges in distribution, the R(k) being sample autocorrelations from a not-necessarily stationary process. The result is used to develop a Quenouille-type goodness-of-fit test based on...

Results of Samuels and Wendel for the simple random walk with drift on the integers which assert independence of interarrival times at the sets {a-r, a+r}, r=1, 2..., k and the arrival position in the set {a-k,a+k}, where a is the starting point, are reobtained by treating the walk as a Markov...