Limit theorems for records from discrete distributions

Weak and strong functional limit theorems are obtained for record values and record epochs in a sequence of independent random variables with common distribution F. The emphasis is on the case in which F is concentrated on the non-negative integers. For contrast, the well-known case of continuous F is also considered. Analogues of results obtained earlier by Resnick, de Haan and the author for continuous F are presented here for F concentrated on the non-negative integers. Also is investigated under which circumstances the latter case is so close to the continuous F case that the resulting limit theorems are the same.