Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A theoretical analysis of one-dimensional discrete generation ensemble
  Kalman particle filters   Despite the widespread usage of discrete generation Ensemble Kalman particle
filtering methodology to solve nonlinear and high dimensional filtering and
inverse problems, little is known about their mathematical foundations. As
genetic-type particle filters (a.k.a. sequential Monte Carlo), this
ensemble-type methodology can also be interpreted as mean-field particle
approximations of the Kalman-Bucy filtering equation. In contrast with
conventional mean-field type interacting particle methods equipped with a
globally Lipschitz interacting drift-type function, Ensemble Kalman filters
depend on a nonlinear and quadratic-type interaction function defined in terms
of the sample covariance of the particles. Most of the literature in applied
mathematics and computer science on these sophisticated interacting particle
methods amounts to designing different classes of useable observer-type
particle methods. These methods are based on a variety of inconsistent but
judicious ensemble auxiliary transformations or include additional
inflation/localisationtype algorithmic innovations, in order to avoid the
inherent time-degeneracy of an insufficient particle ensemble size when solving
a filtering problem with an unstable signal. To the best of our knowledge, the
first and the only rigorous mathematical analysis of these sophisticated
discrete generation particle filters is developed in the pioneering articles by
Le Gland-Monbet-Tran and by Mandel-Cobb-Beezley, which were published in the
early 2010s. Nevertheless, besides the fact that these studies prove the
asymptotic consistency of the Ensemble Kalman filter, they provide exceedingly
pessimistic meanerror estimates that grow exponentially fast with respect to
the time horizon, even for linear Gaussian filtering problems with stable one
dimensional signals. In the present article we develop a novel self-contained
and complete stochastic perturbation analysis of the fluctuations, the
stability, and the long-time performance of these discrete generation ensemble
Kalman particle filters, including time-uniform and non-asymptotic mean-error
estimates that apply to possibly unstable signals. To the best of our
knowledge, these are the first results of this type in the literature on
discrete generation particle filters, including the class of genetic-type
particle filters and discrete generation ensemble Kalman filters. The
stochastic Riccati difference equations considered in this work are also of
interest in their own right, as a prototype of a new class of stochastic
rational difference equation.

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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int