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 Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/17383

 Title: Quasilinear PDEs and forward-backward stochastic differential equations Authors: Wang, Xince Keywords: Forward backward stochastic differential equationsWeak solutionsPartial differential equationsStationary solutionsParabolicEllipticInfinite horizon. Issue Date: 2015 Publisher: © Xince Wang Abstract: In this thesis, first we study the unique classical solution of quasi-linear second order parabolic partial differential equations (PDEs). For this, we study the existence and uniqueness of the $L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{d}) \otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k})\otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k\times d})$ valued solution of forward backward stochastic differential equations (FBSDEs) with finite horizon, the regularity property of the solution of FBSDEs and the connection between the solution of FBSDEs and the solution of quasi-linear parabolic PDEs. Then we establish their connection in the Sobolev weak sense, in order to give the weak solution of the quasi-linear parabolic PDEs. Finally, we study the unique weak solution of quasi-linear second order elliptic PDEs through the stationary solution of the FBSDEs with infinite horizon. Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University. Sponsor: none URI: https://dspace.lboro.ac.uk/2134/17383 Appears in Collections: PhD Theses (Maths)

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