Thesis-2008-Zhang.pdf (2.58 MB)
Stationary solutions of stochastic partial differential equations and infinite horizon backward doubly stochastic differential equations
thesis
posted on 2018-07-20, 11:12 authored by Qi ZhangIn this thesis we study the existence of stationary solutions for stochastic partial
differential equations. We establish a new connection between solutions of backward
doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary
solutions of the SPDEs. For this, we prove the existence and uniqueness of the L2ρ (Rd; R1) × L2ρ (Rd; Rd) valued solutions of BDSDEs with Lipschitz nonlinear term on
both finite and infinite horizons, so obtain the solutions of initial value problems and
the stationary weak solutions (independent of any initial value) of SPDEs. Also the L2ρ (Rd; R1) × L2ρ (Rd; Rd) valued BDSDE with non-Lipschitz term is considered. Moreover,
we verify the time and space continuity of solutions of real-valued BDSDEs, so
obtain the stationary stochastic viscosity solutions of real-valued SPDEs. The connection
of the weak solutions of SPDEs and BDSDEs has independent interests in the areas
of both SPDEs and BSDEs.
History
School
- Science
Department
- Mathematical Sciences
Publisher
© Qi ZhangPublisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2008Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.Language
- en