Nonparametric Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion with Random Effects

Parametric Estimation for Processes Driven by Infinite Dimensional Mixed Fractional Brownian Motion

“…The problem of estimation of parameters for processes driven by processes which are mixtures of independent Brownian and fractional Brownian motions started from the works of Cheridito (2001), Rudomino-Dusyatska (2003) and more recently in Prakasa Rao (2015a,b;2017a,b;2018a,b;, 2020, 2021a among others. Mixed fractional Brownian models were studied in Mishura (2008) and Prakasa Rao (2010) .…”

Maximum likelihood estimation for stochastic differential equations driven by a mixed fractional Brownian motion with random effects

“…They study the properties of kernel and histogram estimators for estimation of the density of random effects. We discussed nonparametric estimation for models governed by stochastic differential equations with random effects driven by a mixed fractional Brownian motion (mfBm) with Hurst index H > 1 2 in Prakasa Rao [21]. For parametric inference for processes driven by mfBm, see Marushkevych [22], Rudomino-Dusyatska [23], Song and Liu [24], Mishra and Prakasa Rao [25], Prakasa Rao [26] and Miao [27] among others.…”