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Large deviations for optimal filtering with fractional Brownian motion

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  • Maroulas, Vasileios
  • Xiong, Jie

Abstract

We establish large deviation estimates for the optimal filter where the observation process is corrupted by a fractional Brownian motion. The observation process is transformed to an equivalent model which is driven by a standard Brownian motion. The large deviations in turn are established by proving qualitative properties of perturbations of the equivalent observation process.

Suggested Citation

  • Maroulas, Vasileios & Xiong, Jie, 2013. "Large deviations for optimal filtering with fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2340-2352.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2340-2352
    DOI: 10.1016/j.spa.2013.02.012
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    References listed on IDEAS

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    1. M.L. Kleptsyna & A. Le Breton, 2002. "Extension of the Kalman–Bucy Filter to Elementary Linear Systems with Fractional Brownian Noises," Statistical Inference for Stochastic Processes, Springer, vol. 5(3), pages 249-271, October.
    2. Sritharan, S.S. & Sundar, P., 2006. "Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1636-1659, November.
    3. Le Breton, Alain, 1998. "Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 263-274, June.
    4. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704, Decembrie.
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    Cited by:

    1. Maroulas, Vasileios & Pan, Xiaoyang & Xiong, Jie, 2020. "Large deviations for the optimal filter of nonlinear dynamical systems driven by Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 203-231.
    2. Cai, Yujie & Huang, Jianhui & Maroulas, Vasileios, 2015. "Large deviations of mean-field stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 1-9.
    3. Gajda, J. & Wyłomańska, A. & Kantz, H. & Chechkin, A.V. & Sikora, G., 2018. "Large deviations of time-averaged statistics for Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 47-55.
    4. Djouadi, Seddik M. & Maroulas, Vasileios & Pan, Xiaoyang & Xiong, Jie, 2017. "Consistency and asymptotics of a Poisson intensity least-squares estimator for partially observed jump–diffusion processes," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 8-16.

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