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

@article{citeulike:4017351, abstract = {We approximate quasi-linear parabolic SPDEs substituting the derivatives in the space variable with finite differences. When the nonlinear terms in the equation are Lipschitz continuous we estimate the rate of Lp convergence of the approximations and we also prove their almost sure uniform convergence to the solution. When the nonlinear terms are not Lipschitz continuous we obtain this convergence in probability, if the pathwise uniqueness for the equation holds.}, author = {Gy\"{o}ngy, Istv\'{a}n}, citeulike-article-id = {4017351}, citeulike-linkout-0 = {http://dx.doi.org/10.1023/A:1008615012377}, citeulike-linkout-1 = {http://www.springerlink.com/content/qr0v2210603u3078}, day = {21}, doi = {10.1023/A:1008615012377}, journal = {Potential Analysis}, keywords = {fd, numerics, spde}, number = {1}, pages = {1--25}, posted-at = {2009-02-06 19:21:29}, priority = {2}, title = {Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations Driven by Space-Time White Noise I}, url = {http://dx.doi.org/10.1023/A:1008615012377}, volume = {9}, year = {1998} }

TY - JOUR ID - citeulike:4017351 L3 - citeulike-article-id:4017351 N2 - We approximate quasi-linear parabolic SPDEs substituting the derivatives in the space variable with finite differences. When the nonlinear terms in the equation are Lipschitz continuous we estimate the rate of Lp convergence of the approximations and we also prove their almost sure uniform convergence to the solution. When the nonlinear terms are not Lipschitz continuous we obtain this convergence in probability, if the pathwise uniqueness for the equation holds. IS - 1 JF - Potential Analysis EP - 25 TI - Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations Driven by Space-Time White Noise I VL - 9 SP - 1 KW - fd KW - numerics KW - spde AU - Gyöngy, István PY - 1998//21/ UR - http://dx.doi.org/10.1023/A:1008615012377 ER -