3:00 p.m., Friday (September 10, 2004)
Math Annex 1100
University of Vienna
Recurrence of stationary random walks
If (X_n) is a (real-valued) stationary process, then the associated (one-dimensional)
random walk is sequence of random variables (Y_n=X_1+\dots +X_n, n\ge 1). The random
walk (Y_n) is recurrent if it comes back to zero (or at least arbitrarily close to zero)
with probability one.
Classical probability theory deals with the case where the random variables (X_n)
are independent and characterizes recurrence of (Y_n) in terms of the distribution
By using methods from ergodic theory one can remove the hypothesis of independence
and obtain very general conditions for recurrence of (Y_n) of arbitrary stationary
random walks in one or more dimensions.
We shall also discuss some of the mysteries associated with recurrence and transience
(i.e. non-recurrence) of stationary and nonstationary random walks.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).