Current trends in asymptotics: some problems and some solutions

AbstractI discuss five topics of current interest in asymptotic analysis: the use of probabilistic methods to estimate the growth of combinatorial sequences, asymptotic methods in the theory of random walks, the asymptotic estimation of solutions of difference equations, asymptotic expansions in generalized scales, and the computation by asymptotic methods of distributions whose moments are known. I give a number of examples and mention some outstanding unsolved problems