Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603266
Title: Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs
Author: Yue, Wen
ISNI:       0000 0004 5356 0466
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2014
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Abstract:
This thesis consists of four parts. In the first part we recall some background theory that will be used throughout the thesis. In the second part, we studied the absolute continuity of the laws of the solutions of some perturbed stochastic differential equaitons(SDEs) and perturbed reflected SDEs using Malliavin calculus. Because the extra terms in the perturbed SDEs involve the maximum of the solution itself, the Malliavin differentiability of the solutions becomes very delicate. In the third part, we studied the absolute continuity of the laws of the solutions of the parabolic stochastic partial differential equations(SPDEs) with two reflecting walls using Malliavin calculus. Our study is based on Yang and Zhang \cite{YZ1}, in which the existence and uniqueness of the solutions of such SPDEs was established. In the fourth part, we gave the existence and uniqueness of the solutions of the elliptic SPDEs with two reflecting walls and general diffusion coefficients.
Supervisor: Zhang, Tusheng Sponsor: School of Mathematics, University of Manchester ; China Scholarship Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.603266  DOI: Not available
Keywords: Stochastic differential equations; Stochastic partial differential equations; Diffusion processes; Peturbed diffusion processes; Reflecting walls; ; Malliavin differentiability; Absolute continuity; Comparison Theorem
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