Large Deviation Rates for Branching Processes--I. Single Type Case

Besides being of some interest in its own right, this seems to be of some importance in algorithmic tree structures in computer science (see [6] and [8]). In [6] it is mentioned that the execution of a canonical algorithm for evaluating uniform AND/OR trees in some probabilistic models can be viewed as a branching process. The probability that the running time of this algorithm deviates from its expected value corresponds to the tail probabilities and large deviations associated with branching processes. Also, from a statistical inference point of view the first quantity above is of some interest