DMS-9500792 Maier The proposed research will apply the tools of singular perturbation theory to the estimation, in various asymptotic limits, of the probability of unlikely events associated with drift-diffusion and other stochastic models. It is often the case that the leading asymptotics of such probabilities are rigorously specified by large deviations theory. Singular perturbation theory, in particular Maslov-WKB theory, permits the formal computation of subdominant asymptotics. Specific stochastic models to be studied include models arising in teletraffic engineering and chemical physics. Physical, chemical, or engineering systems often have a random element. As a consequence, it may be difficult to predict their long-time behavior, or the rate at which unlikely events (large departures from equilibrium, severe equipment malfunction, etc.) are likely to occur. It is important to be able to estimate the frequency of such events. The proposed research will develop and apply mathematical tools to this end.
