Speaker: Alexandra Chronopoulou (Illinois)
Title: Sequential Change Detection for Fractional SDEs
We will consider the problem of sequentially detecting a change in a stochastic process that satisfies a fractional stochastic differential equation with an arbitrary Hurst index, H. For this class of dynamics, we will establish sufficient conditions for the Cumulative Sums (CUSUM) test to be an exact (non-asymptotic) solution to Lorden's minimax optimal stopping problem. In this way, we will extend well-known optimality properties of CUSUM for diffusion processes. The main techniques for these extensions come from fractional calculus and Malliavin calculus.