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Stochastics and Statistics Seminar

Large deviations for random walks under subexponentiality: the big-jump domain

April 18, 2008 @ 11:00 am

Ton Dieker (Georgia Tech I&SE)

Stimulated by applications to internet traffic modeling and insurance mathematics, distributions with heavy tails have been widely studied over the past decades. This talk addresses a fundamental large-deviation problem for random walks with heavy-tailed step-size distributions. We consider so-called subexponential step-size distributions, which constitute the most widely-used class of heavy-tailed distributions. I will present a theory to study sequences {x_n} for which P{S_n>x_n} behaves asymptotically like n P {S_1>x_n} for large n. (joint work with D. Denisov and V. Shneer)

MIT Statistics + Data Science Center
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139-4307