Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion
作者：
Highlights：
• We use random effects to explain the dependence between variables and the variation of variables over time. We consider stochastic differential equations with random effects driven by fractional Brownian motion with long memory characteristics.
• We make use of the maximum likelihood estimation to obtain the exact likelihood function.
• We calculate out the estimates of the unknown mean and variance assuming that obeys Gaussian distribution.
• Our work provides a good solution for the long memory phenomenon in the fields of biomedicine and physics.
摘要
•We use random effects to explain the dependence between variables and the variation of variables over time. We consider stochastic differential equations with random effects driven by fractional Brownian motion with long memory characteristics.•We make use of the maximum likelihood estimation to obtain the exact likelihood function.•We calculate out the estimates of the unknown mean and variance assuming that obeys Gaussian distribution.•Our work provides a good solution for the long memory phenomenon in the fields of biomedicine and physics.
论文关键词：Fractional Brownian motion,Stochastic differential equations,Girsanov-type formula,Random effects,Maximum likelihood estimation
论文评审过程：Received 5 January 2020, Revised 1 December 2020, Accepted 19 December 2020, Available online 11 January 2021, Version of Record 11 January 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125927
