APPLICATION OF CONTINUOUS TIME STOCHASTIC PROCESSES IN SEQUENTIAL CLINICAL RESEARCH DESIGN AND ECONOMETRICS

The principal subject of this thesis is hypothesis testing and related problems of
estimation for stochastic processes. The thesis is concerned in particular with
two areas: sequential hypothesis testing in a Bayesian setting and estimation
of the parameters governing a continuous-time stochastic differential equation
that drives data sampled at high-frequency. The former area is concerned with
hypothesis testing for a newly developed healthcare technology and makes use
of optimal stopping theory. The latter area sees the application of limit theorems for stochastic processes that allow to recover the true volatility process
that can be estimated using the methods of moments estimator.