
Stable filtering procedures for nodal discontinuous Galerkin methods
We prove that the most common filtering procedure for nodal discontinuou...
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Massconservative and positivity preserving secondorder semiimplicit methods for highorder parabolic equations
We consider a class of finite element approximations for fourthorder pa...
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Particle representation for the solution of the filtering problem. Application to the error expansion of filtering discretizations
We introduce a weighted particle representation for the solution of the ...
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Enforcing strong stability of explicit Runge–Kutta methods with superviscosity
A time discretization method is called strongly stable, if the norm of i...
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On the structure preserving highorder approximation of quasistatic poroelasticity
We consider the systematic numerical approximation of Biot's quasistatic...
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Factored Filtering of ContinuousTime Systems
We consider filtering for a continuoustime, or asynchronous, stochastic...
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Geometric Learning and Filtering in Finance
We develop a method for incorporating relevant nonEuclidean geometric i...
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Pathwise approximations for the solution of the nonlinear filtering problem
We consider high order approximations of the solution of the stochastic filtering problem, derive their pathwise representation in the spirit of the earlier work of Clark and Davis and prove their robustness property. In particular, we show that the high order discretised filtering functionals can be represented by Lipschitz continuous functions defined on the observation path space. This property is important from the practical point of view as it is in fact the pathwise version of the filtering functional that is sought in numerical applications. Moreover, the pathwise viewpoint will be a stepping stone into the rigorous development of machine learning methods for the filtering problem. This work is a continuation of a recent work by two of the authors where a discretisation of the solution of the filtering problem of arbitrary order has been established. We expand the previous work by showing that robust approximations can be derived from the discretisations therein.
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