An Introduction to Probability Theory and Its Applications, Volume II

TL;DR: Joint large deviation principle for the empirical pair measure and empirical locality measure of the near intermediate coloured random geometric graph models on n points picked uniformly in a d-dimensional torus of a unit circumference is proved.

TL;DR: A survey of simple applications of renewal theory to problems on random strings and tries is given in this paper, including insertion depth, size, insertion mode and imbalance of tries; variations for b-tries and Patricia tries; Khodak and Tunstall codes.

TL;DR: Two-type age-dependent branching processes with immigration are proposed to model populations of progenitor cells and their differentiated progenies to improve the accuracy of asymptotic approximations to the expectations of the total cell counts.

TL;DR: In this paper, the authors derived upper and lower bounds for the tail of the deficit at ruin in the renewal risk model, which are applicable generally; and (ii) based on reliability classifications.