This research will study the theory of partial sums and partial maxima of independent random variables, probability in Banach spaces and the theory of random sets. The of the three major questions to be viewed will to approximate the distributions of sums of independent random variables. The emphasis will be to obtain results which are widely applicable eg. for random variables taking real or vector values or values in infinite dimensional Banach spaces. The second problem will be to study the partial maxima and their relationship to partial sums. The third problem will be to study unions of independent or dependent random sets and their role in modelling growth phenomena. These models will incorporate a means to alter the activity in a region based on the number of times that a region has been contaminated. Simulations on graphical computer will be done to complement the theoretical work.
