Mathematical Sciences: Asymptotic Expansions, Time Series, and Markov Processes

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The principal investigators will be working on topics in statistics and probability. The first investigator, Dr. Bhattacharya, will continue his work on asymptotic expansions and on large time stability in certain important classes of nonlinear stochastic systems. Asymptotic expansions is a field central to statistics, and the investigator will consider refinements of the Gaussian approximation in central limit theorem motivated by applications, e.g. in analyzing bootstrap methodology. The second topic lies between dynamical systems at one end and nonsingular or irreducible Markov processes at the other. The second investigator, Dr. Chan, will work on problems related to statistical inference for nonstationary time series with infinite variance. This study is motivated by economics, finance, and communications engineering.