Parameter Estimation in Stochastic Differential Equation Driven by Fractional Brownian Motion

Filatova, Darya; Grzywaczewski, M.; Shybanova, E.; Zili, Mounir

doi:10.1109/eurcon.2007.4400579

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…In our experience, the aforementioned estimators work only when estimated from the data on fractional Brownian motion, but unfortunately, in the SDE context, such data are not available. Simulation studies reported in Filatova et al (2007) first estimate H from simulated fractional Brownian motion, and then estimate the other parameters given such estimate of H. In realistic situations this is of course not possible.…”

Section: Discussion On Existing Attempts Regarding Inference In Fract...mentioning

confidence: 99%

Increasing Domain Infill Asymptotics for Stochastic Differential Equations Driven by Fractional Brownian Motion

Maitra¹,

Bhattacharya²

2020

Preprint

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Although statistical inference in stochastic differential equations (SDEs) driven by Wiener process has received significant attention in the literature, inference in those driven by fractional Brownian motion seem to have seen much less development in comparison, despite their importance in modeling long range dependence. In this article, we consider both classical and Bayesian inference in such fractional Brownian motion based SDEs, observed on the time domain [0, T ]. In particular, we consider asymptotic inference for two parameters in this regard; a multiplicative parameter β associated with the drift function, and the so-called "Hurst parameter" H of the fractional Brownian motion, when T → ∞. For unknown H, the likelihood does not lend itself amenable to the popular Girsanov form, rendering usual asymptotic development difficult. As such, we develop increasing domain infill asymptotic theory, by discretizing the SDE into n discrete time points in [0, T ], and letting T → ∞, n → ∞, such that either n/T 2 or n/T tends to infinity. In this setup, we establish consistency and asymptotic normality of the maximum likelihood estimators, as well as consistency and asymptotic normality of the Bayesian posterior distributions. However, classical or Bayesian asymptotic normality with respect to the Hurst parameter could not be established. We supplement our theoretical investigations with simulation studies in a non-asymptotic setup, prescribing suitable methodologies for classical and Bayesian analyses of SDEs driven by fractional Brownian motion.

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Section: Discussion On Existing Attempts Regarding Inference In Fract...mentioning

confidence: 99%

Increasing Domain Infill Asymptotics for Stochastic Differential Equations Driven by Fractional Brownian Motion

Maitra¹,

Bhattacharya²

2020

Preprint

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“…In order to introduce the model for the data description we found the parameters of fBm, using methodology presented in (Filatova, 2008). There was only one significant parameter 0.4501  H (with standard deviation 0.0073 ), which allowed to select a model of the biomass population, namely Next to find estimates of (38) we used ideas of identification methods (Filatova & Grzywaczewski, 2007;Filatova et al, 2007) …”

Section: Examplementioning

confidence: 99%

Fractional Bioeconomic Systems: Optimal Control Problems, Theory and Applications

Filatova¹,

Grzywaczewski²,

Osmolovskii³

2010

Stochastic Control

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Parameter Estimation in Stochastic Differential Equation Driven by Fractional Brownian Motion

Cited by 2 publications

References 13 publications

Increasing Domain Infill Asymptotics for Stochastic Differential Equations Driven by Fractional Brownian Motion

Increasing Domain Infill Asymptotics for Stochastic Differential Equations Driven by Fractional Brownian Motion

Fractional Bioeconomic Systems: Optimal Control Problems, Theory and Applications

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