Speaker
Ludvig Lizana
(Umeå University)
Description
In many applications one wishes to know not only when a
stochastic variable crosses a boundary for the first time,
but also how many times it is crossed in a specific time
interval. While we know the average number of crossings <m>
for discrete stationary Gaussian processes through the well
established Rice formula, we do not know the fluctuations
<m^2> or the distribution of crossing events. We calculate
those quantities analytically from a generalisation of the
so-called Independent Interval approximation, a method where
we assume that the length of time intervals between
successive zero-crossings are uncorrelated. We apply our
results to a discrete version of the Ornstein–Uhlenbeck
process, the autoregressive process, but the Independent
Interval approximation has a much wider applicability. For
example continuous non-stationary Gaussian processes.
