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Pathwise Approximations for the Solution of the Non-Linear Filtering Problem

In: Stochastic Analysis, Filtering, and Stochastic Optimization

Author

Listed:
  • Dan Crisan

    (Imperial College London, Huxley’s Building, Department of Mathematics)

  • Alexander Lobbe

    (University of Oslo, Department of Mathematics)

  • Salvador Ortiz-Latorre

    (University of Oslo, Department of Mathematics)

Abstract

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 [2] and Davis [10, 11] 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 viewpointwill be a stepping stone into the rigorous development ofmachine learning methods for the filtering problem. This work is a cotinuation of [5] where a discretisation of the solution of the filtering problem of arbitrary order has been established. We expand the work in [5] by showing that robust approximations can be derived from the discretisations therein.

Suggested Citation

  • Dan Crisan & Alexander Lobbe & Salvador Ortiz-Latorre, 2022. "Pathwise Approximations for the Solution of the Non-Linear Filtering Problem," Springer Books, in: George Yin & Thaleia Zariphopoulou (ed.), Stochastic Analysis, Filtering, and Stochastic Optimization, pages 79-99, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98519-6_4
    DOI: 10.1007/978-3-030-98519-6_4
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