Refreshments: 3:30 - 4:00 p.m. Friday,
September 24, at 327 Yost Talk: 4:00 - 5:00 p.m. Friday, September 24, at 327 Yost.
Levy processes are building blocks of various stochastic models,
including certain models with heavy tailed distributions.
Computer simulation as well as theoretical analysis of such models
presents a problem when the L\'evy processes has infinitely many jumps.
The usual approximation by discrete random walks does not converge in
the uniform metric because one is always missing large jumps under
deterministic time steps.
In this talk we will discuss the method of the uniform approximation
of Levy processes by means of series expansions. Specifically,
we will discuss series expansions without compensation which are
based on Poissonian truncation of i.i.d. sequences.
By an appropriate choice of the truncation function (and
possibly an optional randomization) one obtains series
expansions without compensation for many L\'evy processes, including
all processes with infinite variation of positive and negative jumps.
We will also mention a different idea of approximation, and its
limitations, of the small jump part of L\'evy processes by Brownian
motion.
Questions? Nidhan Choudhuri