Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations driven by Space-Time White Noise II Export

@article{citeulike:4017260, 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.}, author = {Gy\"{o}ngy, Istv\'{a}n}, citeulike-article-id = {4017260}, citeulike-linkout-0 = {http://dx.doi.org/10.1023/A:1008699504438}, citeulike-linkout-1 = {http://www.springerlink.com/content/x644l10403753878}, day = {1}, doi = {10.1023/A:1008699504438}, journal = {Potential Analysis}, keywords = {numerics, spde}, number = {1}, pages = {1--37}, posted-at = {2009-02-06 19:06:00}, priority = {2}, title = {Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations driven by Space-Time White Noise II}, url = {http://dx.doi.org/10.1023/A:1008699504438}, volume = {11}, year = {1999} }

TY - JOUR ID - citeulike:4017260 L3 - citeulike-article-id:4017260 N2 - 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. IS - 1 JF - Potential Analysis EP - 37 TI - Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations driven by Space-Time White Noise II VL - 11 SP - 1 KW - numerics KW - spde AU - Gyöngy, István PY - 1999//01/ UR - http://dx.doi.org/10.1023/A:1008699504438 ER -