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Existence and uniqueness for variational data assimilation in continuous time

Bröcker, J. (2021) Existence and uniqueness for variational data assimilation in continuous time. Mathematical Control & Related Fields. ISSN 2156-8472 (In Press)

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To link to this item DOI: 10.3934/mcrf.2021050

Abstract/Summary

A variant of the optimal control problem is considered which is nonstandard in that the performance index contains "stochastic" integrals, that is, integrals against very irregular functions. The motivation for considering such performance indices comes from dynamical estimation problems where observed time series need to be "fitted" with trajectories of dynamical models. The observations may be contaminated with white noise, which gives rise to the nonstandard performance indices. Problems of this kind appear in engineering, physics, and the geosciences where this is referred to as data assimilation. The fact that typical models in the geosciences do not satisfy linear growth nor monotonicity conditions represents an additional difficulty. Pathwise existence of minimisers is obtained, along with a maximum principle as well as preliminary results in dynamic programming. The results also extend previous work on the maximum aposteriori estimator of trajectories of diffusion processes.

Item Type:Article
Refereed:Yes
Divisions:Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE)
Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:100788
Publisher:American Institute of Mathematical Sciences

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