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See detailStatistical inference for Vasicek-type model driven by Hermite processes
Nourdin, Ivan UL; Tran, Thi Thanh Diu UL

in Stochastic Processes and Their Applications (2019), 129(10), 3774-3791

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See detailContributions to the asymptotic study of Hermite driven processes
Tran, Thi Thanh Diu UL

Doctoral thesis (2018)

This thesis consists of two parts. Part I is an introduction to Hermite processes, Hermite random fields, Fisher information and to the papers constituting the thesis. More precisely, in Section 1 we ... [more ▼]

This thesis consists of two parts. Part I is an introduction to Hermite processes, Hermite random fields, Fisher information and to the papers constituting the thesis. More precisely, in Section 1 we introduce Hermite processes in a nutshell, as well as some of its basic properties. It is the necessary background for the articles [a] and [c]. In Section 2 we consider briefly the multiparameter Hermite random fields and we study some less elementary facts which are used in the article [b]. In section 3, we recall some terminology about Fisher information related to the article [d]. Finally, our articles [a] to [d] are summarised in Section 4. Part II consists of the articles themselves: [a] T.T. Diu Tran (2017): Non-central limit theorem for quadratic functionals of Hermite-driven long memory moving average processes. Stochastic and Dynamics, 18, no. 4. [b] T.T. Diu Tran (2016): Asymptotic behavior for quadratic variations of nonGaussian multiparameter Hermite random fields. Under revision for Probability and Mathematical Statistics. [c] I. Nourdin, T.T. Diu Tran (2017): Statistical inference for Vasicek-type model driven by Hermite processes. Submitted to Stochastic Process and their Applications. [d] T.T. Diu Tran (2017+): Fisher information and multivariate Fouth Moment Theorem. Main results have already been obtained. It should be submitted soon. [less ▲]

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