Abstract:
The talk considers two classical problems of statistical sequential analysis: sequential hypothesis testing and the disorder detection (changepoint detection) problem. These problems have been extensively studied in the literature for standard Brownian motion and other diffusion processes. In our work they are investigated for fractional Brownian motion — a Gaussian process with dependent increments that generalizes standard Brownian motion and is widely used in applications. A key difficulty is that fractional Brownian motion is neither a Markov process nor a semimartingale, which prevents the direct application of classical methods of stochastic analysis. To address these problems, it is necessary to combine tools from the theory of Gaussian processes, fractional calculus, optimal control, and machine learning. The talk is based on joint work with A. N. Shiryaev and A. A. Muravlev.
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