Title:
Efficient Simulation For Tail Probabilities Of Gaussian Random Fields
Abstract:
We are interested in computing tail probabilities for the maxima of
Gaussian random fields. In this paper, we discuss two special cases:
random fields defined over a finite number of distinct point and
fields with finite Karhunen-Lo\`{e}ve expansions. For the first case
we propose an importance sampling estimator which yields
asymptotically zero relative error. Moreover, it yields a procedure
for sampling the field conditional on it having an excursion above a
high level with a complexity that is uniformly bounded as the level
increases. In the second case we propose an estimator which is
asymptotically optimal. These results serve as a first step analysis
of rare-event simulation for Gaussian random fields.