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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Zachary William Bezemek\nBoston University\n\nAbstract: We cons
ider an ensemble of N interacting particles modeled by a system of N stocha
stic differential equations (SDEs). The coefficients of the SDEs are taken
to be such that as N approaches infinity\, the system undergoes Kacâ€™s propa
gation of chaos\, and hence is well-approximated by the solution to a McKea
n-Vlasov Equation. Rare but possible deviations of the behavior of the part
icles from this limit may reflect a catastrophe\, and computing the probabi
lity of such rare events is of high interest in many applications.\nIn this
talk\, we design an importance sampling scheme which allows us to numerica
lly compute statistics related to these rare events with high accuracy and
efficiency for any N. Standard Monte Carlo methods behave exponentially poo
rly as N increases for such problems. Our scheme is based on subsolutions o
f a Hamilton-Jacobi-Bellman (HJB) Equation on Wasserstein Space which arise
s in the theory of mean-field control. This HJB Equation is seen to be conn
ected to the large deviations rate function for the empirical measure on th
e ensemble of particles. We identify conditions under which our scheme is p
rovably asymptotically optimal in N in the sense of log-efficiency. We also
provide evidence\, both analytical and numerical\, that with sufficient re
gularity of the solution to the HJB Equation\, our scheme can have vanishin
gly small relative error as N increases.
DTEND:20230114T003000Z
DTSTAMP:20240523T152834Z
DTSTART:20230113T233000Z
LOCATION:
SEQUENCE:0
SUMMARY:Joint Math Finance Colloquium and Probability/Statistics Seminar: L
arge Deviations and Importance Sampling for Weakly Interacting Diffusions
UID:tag:localist.com\,2008:EventInstance_42049356491771
URL:https://calendar.usc.edu/event/joint_math_finance_colloquium_and_probab
ilitystatistics_seminar_large_deviations_and_importance_sampling_for_weakly
_interacting_diffusions
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