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Numerical Analysis Seminar
Seminar information archive ～12/28｜Next seminar｜Future seminars 12/29～
| Date, time & place | Tuesday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Norikazu Saito, Takahito Kashiwabara |
2025/12/16
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Laurent Mertz (City University of Hong Kong)
A Control Variate Method Driven by Diffusion Approximation (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Laurent Mertz (City University of Hong Kong)
A Control Variate Method Driven by Diffusion Approximation (English)
[ Abstract ]
We present a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic forces. The control variate is the expectation of the same functional for the limit diffusion process that approximates the original process when the mean-reversion time goes to zero. To get an efficient control variate estimator, we propose a coupling method to build the original process and the limit diffusion process. We show that the correlation between the two processes indeed goes to one when the mean reversion time goes to zero and we quantify the convergence rate, which makes it possible to characterize the variance reduction of the proposed control variate method. The efficiency of the method is illustrated on a few examples. This is joint work with Josselin Garnier (École Polytechnique, France). Link to the paper: https://doi.org/10.1002/cpa.21976
[ Reference URL ]We present a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic forces. The control variate is the expectation of the same functional for the limit diffusion process that approximates the original process when the mean-reversion time goes to zero. To get an efficient control variate estimator, we propose a coupling method to build the original process and the limit diffusion process. We show that the correlation between the two processes indeed goes to one when the mean reversion time goes to zero and we quantify the convergence rate, which makes it possible to characterize the variance reduction of the proposed control variate method. The efficiency of the method is illustrated on a few examples. This is joint work with Josselin Garnier (École Polytechnique, France). Link to the paper: https://doi.org/10.1002/cpa.21976
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
