Large Deviation Probabilities for Maximum Likelihood Estimator and Bayes Estimator of a Parameter for Mixed Fractional Ornstein-Uhlenbeck Type Process

Abstract

We investigate the probabilities of large deviations of the maximum likelihood estimator and Bayes estimator of the drift parameter for a mixed fractional Ornstein-Uhlenbeck type process.

Maximum likelihood estimation for stochastic differential equations driven by a mixed fractional Brownian motion with 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. El Omari et al [28] studied estimation of parameters µ and σ 2 when the random effects are Gaussian with mean µ and variance σ 2 based on discrete observations on the process.…”

Nonparametric Estimation of Linear Multiplier for Processes Driven by Mixed fractional Brownian Motion

“…Some applications of such models in finance are presented in Prakasa Rao (2015 a,b). For related work on parametric inference for processes driven by mfBm, see Marushkevych (2016), Rudomino-Dusyatska (2003), Song and Lin (2014), Mishra and Prakasa Rao (2017), Prakasa Rao (2009) and Miao (2010) among others. Nonparametric estimation of the trend coefficient in models governed by stochastic differential equations driven by a mixed fractional Brownian motion is investigated in Prakasa Rao (2018b).…”