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A strongly convergent numerical scheme from EnKF continuum analysis | | Dirk Blömker
; Claudia Schillings
; Philipp Wacker
; | | Date: |
20 Mar 2017 | | Abstract: | The Ensemble Kalman methodology in an inverse problems setting can be viewed
-- when constructed in a sequential Monte-Carlo-like manner -- yields a
iterative scheme, which is a weakly tamed discretization scheme for a certain
stochastic differential equation (SDE) for which Schillings and Stuart proved
several properties. Assuming a suitable approximation result, dynamical
properties of the SDE can be rigorously pulled back via the discrete scheme to
the original Ensemble Kalman filter.
This paper makes a step towards closing the gap of a missing approximation
result by proving a strong convergence result. We focus here on a simplified
model with similar properties than the one arising in the Ensemble Kalman
filter, which can be viewed as a single particle filter for a linear map.
Our method has many paralles with the bootstrapping method introduced by
Hutzenthaler and Jentzen, although we use stopping times instead of working
with indicator functions on suitable heavy-mass sets. This is similar to a
technique employed by Higham, Mao and Stuart, although our approach differs
from theirs in that we have to avoid applying Gronwall’s inequality. | | Source: | arXiv, 1703.6767 | | Services: | Forum | Review | PDF | Favorites | |
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