My general research interests are in applied probability and statistics: stochastic processes, long-range dependent and heavy-tailed models, self-similarity, stable processes, max-stable processes, and their applications to Internet traffic modeling, computer science and finance.
My most recent interests revolve around high-dimensional and functional data, function-valued stochastic processes, their modeling, inference, and applications to oceanography. At the same time, I continue to be very interested in extreme value theory, heavy-tails, and long-range dependent processes and random fields.
Probability
My early work focuses on alpha-stable infinite variance processes as well as self-similar and long-range dependent stochastic processes such as the fractional Brownian motion and FARIMA time series. More recently, I have worked on extreme value theory — the representations, ergodic properties, structure and classification of max-stable processes and random fields. Exciting applications of max-stable processes and random fields arise in many fields where extremes and maxima are of interest.
Statistics and Applications
Internet traffic modeling, streaming data, estimation of the tail exponent and the extremal index. Prediction in max-stable models. Spatial statisitcs and wavelets.
Computing
Efficient simulation of stochastic processes: FARIMA time series, fractional Brownian motion, multifractional Brownian motion, linear fractional stable motions, max-stable processes and random fields. Computational prediction in max-stable random fields.
For more details and free Matlab and R code, click on the Software tab above.
