Article2011

Parametric Estimation for SDEs With Additive Sub-Fractional Brownian Motion ∗

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Stochastic processes and financial applications Fractional Differential Equations Solutions Fuzzy Systems and Optimization

Abstract

We study the maximum likelihood estimator for stochastic differential equations with additive sub-fractional Brownian motion. The study applies Girsanov transform to the sub-fractional Brownian motion and employs the theory of regularity and supremum estimation for Gaussian process.

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References

1976Stochastic Differential Equations and Applications 1999Stochastic Analysis of the Fractional Brownian Motion 1999An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian Motions 1999Statistical inference for diffusion type processes 2004A series expansion of fractional Brownian motion 2008On the Wiener integral with respect to a sub-fractional Brownian motion on an interval 2000Parameter Estimation and Optimal Filtering for Fractional Type Stochastic Systems 2003Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion

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2018Least squares estimation for the drift parameters in the sub-fractional Vasicek processes 2021Parameter Estimation for an Ornstein-Uhlenbeck Process Driven by a General Gaussian Noise 2016On some maximal and integral inequalities for sub-fractional Brownian motion 2016Least squares estimation for ornstein-uhlenbeck processes driven by the weighted fractional brownian motion

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