TY - JOUR
T1 - Escaping from an attractor
T2 - Importance sampling and rest points i
AU - Dupuis, Paul
AU - Spiliopoulos, Konstantinos
AU - Zhou, Xiang
PY - 2015/10
Y1 - 2015/10
N2 - We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complicates the analysis is that rest points are included in the domain of interest. We build importance sampling schemes with provably good performance both pre-asymptotically, that is, for fixed size of the noise, and asymptotically, that is, as the size of the noise goes to zero, and that do not degrade as the time horizon gets large. Simulation studies demonstrate the theoretical results.
AB - We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complicates the analysis is that rest points are included in the domain of interest. We build importance sampling schemes with provably good performance both pre-asymptotically, that is, for fixed size of the noise, and asymptotically, that is, as the size of the noise goes to zero, and that do not degrade as the time horizon gets large. Simulation studies demonstrate the theoretical results.
KW - Attractors
KW - Equilibrium points
KW - Importance sampling
KW - Large deviations
KW - Monte Carlo methods
UR - http://www.scopus.com/inward/record.url?scp=84941585040&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84941585040&origin=recordpage
U2 - 10.1214/14-AAP1064
DO - 10.1214/14-AAP1064
M3 - 21_Publication in refereed journal
VL - 25
SP - 2909
EP - 2958
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 5
ER -