Colloquium
3:00 p.m., Friday (September 10, 2004)
Math Annex 1100
Klaus Schmidt
University of Vienna
Recurrence of stationary random walks
If (X_n) is a (realvalued) stationary process, then the associated (onedimensional)
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
of X_1.
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. nonrecurrence) of stationary and nonstationary random walks.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
