Maximum Likelihood Estimation of Stochastic Differential Equations with Random Effects Driven by Fractional Brownian Motion

2020/01/06 by Min Dai, Dai, Min, Jinqiao Duan +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2001.01412

openalex publication_date 2020/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Statistics of Random Processes
• Nonlinear Mixed Effects Models for Repeated Measures Data

Cited by

• Fixed-Point Estimation of the Drift Parameter in Stochastic Differential Equations Driven by Rough Multiplicative Fractional Noise

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