dc.contributor.advisor Hu, Yaozhong dc.contributor.author Hu, Guannan dc.date.accessioned 2016-10-12T02:39:26Z dc.date.available 2016-10-12T02:39:26Z dc.date.issued 2015-12-31 dc.date.submitted 2015 dc.identifier.other http://dissertations.umi.com/ku:14276 dc.identifier.uri http://hdl.handle.net/1808/21696 dc.description.abstract Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness of the solution and calculate the moment bounds of the solution when the noise has Reisz kernel as space covariance. Along the way, we obtain some new properties of the fundamental solutions. Chapter 4 studies the time-fractional diffusion with fractional Gaussian noise. We obtain conditions so that the square integrable solution exists uniquely. Chapter 5 studies the time-fractional diffusion where the Gaussian noise is general in time with space covariance given by fractional, Riesz and Bessel kernel. dc.format.extent 121 pages dc.language.iso en dc.publisher University of Kansas dc.rights Copyright held by the author. dc.subject Mathematics dc.subject chaos expansion dc.subject Fox's H-function; dc.subject fractional derivative dc.subject Green's functions dc.subject mild solution dc.subject multiple integral of the Itô type dc.title Fractional Diffusion in Gaussian Noisy Environment dc.type Dissertation dc.contributor.cmtemember Nualart, David dc.contributor.cmtemember Soo, Terry dc.contributor.cmtemember Tu, Xuemin dc.contributor.cmtemember Huan, Luke dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel Ph.D. kusw.oanotes 2017/10/04: The ETD release form is attached to this record as a license file. dc.identifier.orcid dc.rights.accessrights openAccess
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