A stability vs. Monte-Carlo integration problem for SDEs
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
Warwick EPSRC Symposium: Stochastic PDEs
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
In this work we investigate the interplay of almost sure and mean-square stability for
linear SDEs and the Monte Carlo method for estimating the second moment of the solution
process. In the situation where the zero solution of the SDE is asymptotically stable in
the almost sure sense but asymptotically mean-square unstable, the latter property is
determined by rarely occurring trajectories that are sufficiently far away from the origin.
The standard Monte Carlo approach for estimating higher moments essentially computes
a finite number of trajectories and is bound to miss those rare events. It thus fails to
reproduce the correct mean-square dynamics (under reasonable cost). A straightforward
application of variance reduction techniques will typically not resolve the situation unless
these methods force the rare, exploding trajectories to happen more frequently. Here
we propose an appropriately tuned importance sampling technique based on Girsanov?s
theorem to deal with the rare event simulation. In addition further variance reduction
techniques, such as multilevel Monte Carlo, can be applied to control the variance of the
modified Monte Carlo estimators. As an illustrative example we discuss the numerical
treatment of the stochastic heat equation with multiplicative noise and present simulation
results.
Sprache der Kurzfassung:
Englisch
Vortragstyp:
Hauptvortrag / Eingeladener Vortrag auf einer Tagung
Forschungs-