Strong Convergence Rate of Finite Difference Approximations for Stochastic Cubic Schr\"odinger Equations

[1]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[2]  O. Bang,et al.  The influence of noise on critical collapse in the nonlinear Schrödinger equation , 1995 .

[3]  I. Gyöngy.  Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations Driven by Space-Time White Noise I , 1998 .

[4]  I. Gyöngy.  Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations driven by Space-Time White Noise II , 1999 .

[5]  A. Debussche,et al.  Numerical simulation of focusing stochastic nonlinear Schrödinger equations , 2002 .

[6]  A. Debussche,et al.  The Stochastic Nonlinear Schrödinger Equation in H 1 , 2003 .

[7]  Arnaud Debussche,et al.  A semi-discrete scheme for the stochastic nonlinear Schrödinger equation , 2004, Numerische Mathematik.

[8]  Jonathan C. Mattingly,et al.  Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing , 2004, math/0406087.

[9]  A. Kebaier,et al.  Statistical Romberg extrapolation: A new variance reduction method and applications to option pricing , 2005, math/0602529.

[10]  A. D. Bouard,et al.  Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation , 2006 .

[11]  M. Röckner,et al.  A Concise Course on Stochastic Partial Differential Equations , 2007 .

[12]  J. Zabczyk,et al.  Stochastic Equations in Infinite Dimensions , 2008 .

[13]  Nicolai V. Krylov,et al.  Accelerated Finite Difference Schemes for Linear Stochastic Partial Differential Equations in the Whole Space , 2010, SIAM J. Math. Anal..

[14]  Stig Larsson,et al.  Finite Element Approximation of the Cahn-Hilliard-Cook Equation , 2011, SIAM J. Numer. Anal..

[15]  Philipp Dörsek,et al.  Semigroup Splitting and Cubature Approximations for the Stochastic Navier-Stokes Equations , 2011, SIAM J. Numer. Anal..

[16]  Arnulf Jentzen,et al.  Galerkin Approximations for the Stochastic Burgers Equation , 2013, SIAM J. Numer. Anal..

[17]  M. Hutzenthaler,et al.  Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations , 2013, 1309.5595.

[18]  Jialin Hong,et al.  Convergence of a $$\theta $$θ-scheme to solve the stochastic nonlinear Schrödinger equation with Stratonovich noise , 2014, 1410.6231.

[19]  M. Hutzenthaler,et al.  On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients , 2014, 1401.0295.

[20]  M. Röckner,et al.  Stochastic Partial Differential Equations: An Introduction , 2015 .

[21]  S. Larsson,et al.  On the discretisation in time of the stochastic Allen–Cahn equation , 2015, 1510.03684.

[22]  Sebastian Becker,et al.  An Exponential Wagner-Platen Type Scheme for SPDEs , 2013, SIAM J. Numer. Anal..

[23]  Sebastian Riedel,et al.  From Rough Path Estimates to Multilevel Monte Carlo , 2013, SIAM J. Numer. Anal..

[24]  Xiaojie Wang,et al.  Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise , 2015, 1503.00073.

[25]  Jialin Hong,et al.  Symplectic Runge-Kutta Semidiscretization for Stochastic Schrödinger Equation , 2016, SIAM J. Numer. Anal..

[26]  Zhihui Liu,et al.  Approximating Stochastic Evolution Equations with Additive White and Rough Noises , 2016, SIAM J. Numer. Anal..

[27]  Jialin Hong,et al.  Finite element approximations for second-order stochastic differential equation driven by fractional Brownian motion , 2015, 1507.02399.