dc.contributor.advisor Nualart, David dc.contributor.advisor Hu, Yaozhong dc.contributor.author ZHOU, HONGJUAN dc.date.accessioned 2019-05-12T19:38:51Z dc.date.available 2019-05-12T19:38:51Z dc.date.issued 2018-05-31 dc.date.submitted 2018 dc.identifier.other http://dissertations.umi.com/ku:15961 dc.identifier.uri http://hdl.handle.net/1808/27944 dc.description.abstract This dissertation systematically considers the inference problem for stochastic differential equations (SDE) driven by fractional Brownian motion. For the volatility parameter and Hurst parameter, the estimators are constructed using iterated power variations. To prove the strong consistency and the central limit thoerems of the estimators, the asymptotics of the power variatons are studied, which include the strong consistency, central limit theorem, and the convergence rate for the iterated power variations of the Skorohod integrals with respect to fractional Brownian motion. The iterated logarithm law of the power variations of fractional Brownian motion is proved. The joint convergence along different subsequence of power variations of Skorohod integrals is also studied in order to derive the central limit theorem for the estimators. Another important topic considered in this dissertation is the estimation of drift parameters of the SDEs. A least squares estimator (LSE) is proposed and the strong consistency is proved for the fractional Ornstein-Uhlenbeck process that is the solution to the linear SDE. The fourth moment theorem is applied to obtain the central limit theorems. Then the LSE is considered for the drift parameter of the multi-dimensional nonlinear SDE. While proving the strong consistency of LSE, the regularity structure of the SDE’s solution is explored and the maximal inequality for the Skorohod integrals is derived. The main tools used in this research are Malliavin calculus and some Gaussian analysis elements. dc.format.extent 145 pages dc.language.iso en dc.publisher University of Kansas dc.rights Copyright held by the author. dc.subject Mathematics dc.subject Statistics dc.subject fractional Brownian motion dc.subject Malliavin calculus dc.subject parameter estimation dc.subject power variation dc.subject stochastic differential equation dc.title Parameter estimation for stochastic differential equations driven by fractional Brownian motion dc.type Dissertation dc.contributor.cmtemember Liu, Zhipeng dc.contributor.cmtemember Soo, Terry dc.contributor.cmtemember Zhang, Jianbo dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel Ph.D. dc.identifier.orcid dc.rights.accessrights openAccess
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