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AIMS Mathematics

2022, Volume 7, Issue 7: 12952-12961. doi: 10.3934/math.2022717
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Research article

Parameter estimation for partially observed stochastic differential equations driven by fractional Brownian motion

  • School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, China
  • Received: 07 January 2022 Revised: 06 April 2022 Accepted: 24 April 2022 Published: 07 May 2022

  • MSC : 60H10, 62F12

  • This paper is concerned with parameter estimation for partially observed stochastic differential equations driven by fractional Brownian motion. Firstly, the state estimation equation is given and the parameter estimator is derived. Then, the strong consistency and asymptotic normality of the maximum likelihood estimator are derived by applying the strong law of large numbers for continuous martingales and the central limit theorem for stochastic integrals with respect to Gaussian martingales. Finally, an example is provided to verify the results.

    Citation: Chao Wei. Parameter estimation for partially observed stochastic differential equations driven by fractional Brownian motion[J]. AIMS Mathematics, 2022, 7(7): 12952-12961. doi: 10.3934/math.2022717

    Related Papers:

  • This paper is concerned with parameter estimation for partially observed stochastic differential equations driven by fractional Brownian motion. Firstly, the state estimation equation is given and the parameter estimator is derived. Then, the strong consistency and asymptotic normality of the maximum likelihood estimator are derived by applying the strong law of large numbers for continuous martingales and the central limit theorem for stochastic integrals with respect to Gaussian martingales. Finally, an example is provided to verify the results.


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