Research
My research lies at the intersection of extreme value theory, stochastic processes, time series, and asymptotic statistics. I am particularly interested in how nonstandard dependence structures affect both statistical inference and probabilistic models for rare events.
Extremes in long memory time series
Long-range dependence creates persistent extremal dependence that falls outside many of the mixing and anti-clustering frameworks commonly used in extreme value theory. My work develops reduction principles and central limit theory for threshold-based statistics in long memory linear processes, including the Hill estimator and serial tail-dependence estimators. My current focus is on developing statistical inference methods based on these results.
Stationary models for extremal processes
I study particle system constructions of stationary max-infinitely divisible processes. As a first step, I developed a construction using random, state-dependent time changes of the underlying particles to modify the temporal dependence structure of the resulting max-id processes while preserving stationarity and the limiting max-stable process. This connects techniques from the theory of Markov processes, Poisson particle systems, and extreme value theory. My current focus is on extending this construction to random fields.