首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations driven by Space-Time White Noise II
Authors:Gyöngy  István
Institution:(1) Department of Mathematics and Statistics, The University of Edinburgh, Edinburgh, EH9 3JZ, U.K. e-mail
Abstract:We approximate quasi-linear parabolic SPDEs substituting the derivatives with finite differences. We investigate the resulting implicit and explicit schemes. For the implicit scheme we estimate the rate of Lp convergence of the approximations and we also prove their almost sure convergence when the nonlinear terms are Lipschitz continuous. When the nonlinear terms are not Lipschitz continuous we obtain convergence in probability provided pathwise uniqueness for the equation holds. For the explicit scheme we get these results under an additional condition on the mesh sizes in time and space.
Keywords:Stochastic partial differential equations  finite-difference approximations  
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号