UCSD MATHEMATICS DEPARTMENT: PROBABILITY SEMINAR
Taboo Stationarity
Hermann Thorisson,
University of Iceland
Abstract:
In this talk we consider the taboo counterpart of
stationarity.
Stationarity is the characterizing property of any two-
sided limit process
obtained by shifting the time-origin of a one-sided
process to the far
future. Similarly, taboo stationarity is the
characterizing property of any
two-sided limit process obtained by shifting the origin
of a one-sided
process to the far future under taboo, that is,
conditionally on the
process not having entered a taboo region of its state
space up to the new
time-origin. This is, for instance, an appropriate model
for a fish
population that has lived a long time in an isolated
lake, will eventually
become extinct, but is still non-extinct at the time of
observation.
We present a basic but amazingly simple structural
characterization of
taboo stationary processes and then take a closer look at
the structure in
the regenerative case.
Reference:
Thorisson, H. (2000): Coupling, Stationarity, and
Regeneration. Springer, New York