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Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion. (English) Zbl 1508.62062

Summary: 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 \(X_i(t)\) 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.

MSC:

62F10 Point estimation
60G22 Fractional processes, including fractional Brownian motion
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Software:

MsdeParEst; GitHub
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Full Text: DOI arXiv

References:

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