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Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion

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  • Le Breton, Alain

Abstract

The optimal filter is derived in a Gaussian linear system where the signal is a fixed random variable and the observation is driven by a fractional Brownian motion. An application to a related parameter estimation problem is discussed and a Girsanov-type formula is investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:3:p:263-274
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    Citations

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    Cited by:

    1. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    2. Liu, Yanghui & Nualart, Eulalia & Tindel, Samy, 2019. "LAN property for stochastic differential equations with additive fractional noise and continuous time observation," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2880-2902.
    3. 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.
    4. Chigansky, Pavel & Kleptsyna, Marina, 2018. "Exact asymptotics in eigenproblems for fractional Brownian covariance operators," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2007-2059.
    5. Nenghui Kuang & Huantian Xie, 2015. "Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 75-91, February.
    6. Mandrekar, V. & Naik-Nimbalkar, U.V., 2009. "Identification of a Markovian system with observations corrupted by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 965-968, April.
    7. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.
    8. Bertin, Karine & Torres, Soledad & Tudor, Ciprian A., 2011. "Drift parameter estimation in fractional diffusions driven by perturbed random walks," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 243-249, February.
    9. Laurini, Márcio Poletti & Hotta, Luiz Koodi, 2013. "Indirect Inference in fractional short-term interest rate diffusions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 109-126.
    10. M. Mishra & B. Prakasa Rao, 2011. "Nonparametric estimation of trend for stochastic differential equations driven by fractional Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 101-109, May.

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