Repository: Freie Universität Berlin, Math Department

Continuous time limit of the stochastic ensemble Kalman inversion: Strong convergence analysis

Blömker, Dirk and Schillings, Claudia and Wacker, Philipp and Weissmann, Simon (2021) Continuous time limit of the stochastic ensemble Kalman inversion: Strong convergence analysis. . . (Submitted)

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Official URL: https://doi.org/10.48550/arXiv.2107.14508

Abstract

The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively applies the ensemble Kalman update to evolve (the approximation of the) prior into the posterior measure. For the convergence analysis of the EKI it is common practice to derive a continuous version, replacing the iteration with a stochastic differential equation. In this paper we validate this approach by showing that the stochastic EKI iteration converges to paths of the continuous-time stochastic differential equation by considering both the nonlinear and linear setting, and we prove convergence in probability for the former, and convergence in moments for the latter. The methods employed can also be applied to the analysis of more general numerical schemes for stochastic differential equations in general.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:2829
Deposited By: Ulrike Eickers
Deposited On:04 May 2022 05:50
Last Modified:04 May 2022 05:50

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