The Principal Investigator will study sums of independent random variables. The research will focus primarily on identifying the best possible constants in inequalities for moments and tail probabilities for such sums. The case of randomly stopped sums will be investigated as well. The Principal Investigator will study certain problems concerning sums of random variables. A primary focus of the proposed research is to establish precise quantitative information on the behavior of such sums. A more complex situation, in which a number of summands is itself a random quantity, will be investigated as well.
