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Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion

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  • Dai, Min
  • Duan, Jinqiao
  • Liao, Junjun
  • Wang, Xiangjun

Abstract

Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by the stochastic differential equations with drift term relying on some random effects. We obtain the Girsanov-type formula of the stochastic differential equation driven by Fractional Brownian Motion through kernel transformation. Under some assumptions of the random effect, we estimate the parameter estimators by the maximum likelihood estimation and give some numerical simulations for the discrete observations. Results show that for the different H, the parameter estimator is closer to the true value as the amount of data increases.

Suggested Citation

  • Dai, Min & Duan, Jinqiao & Liao, Junjun & Wang, Xiangjun, 2021. "Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308808
    DOI: 10.1016/j.amc.2020.125927
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    References listed on IDEAS

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    1. Comte, F. & Genon-Catalot, V. & Samson, A., 2013. "Nonparametric estimation for stochastic differential equations with random effects," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2522-2551.
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    Cited by:

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