Mathematical Sciences: Studies on Markov Chains and Branching Processes

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Research will continue in the areas of nonlinear filtering, Markov chains, and branching processes. In nonlinear filtering, approximations will be studied and comparisons will be made between various approximations. For Markov chains on a general state space, consistent and asymptotically normal estimates of the transition function are to be sought. Large deviations of the estimates of the population in a supercritical branching process will also be investigated. Research will be done on distinguishing between the original signal and interference when a signal has been received. In addition, attempts will be made to estimate the probability structure of certain types of randomly evolving processes.