On the splitting method for some complex-valued quasilinear evolution equations

Zdzislaw Brzezniak (1) , Annie Millet (2, 3)

1 University of York [York, UK]
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Using the approach of the splitting method developed by I. Gyöngy and N. Krylov for parabolic quasi linear equations, we study the speed of convergence for general complex-valued stochastic evolution equations. The approximation is given in general Sobolev spaces and the model considered here contains both the parabolic quasi-linear equations under some (non strict) stochastic parabolicity condition as well as linear Schrödinger equations

Keywords: Stochastic evolution equations; Schrödinger equation; splitting method; speed of convergence; discretization scheme

Domains: Probability [math.PR]

Zdzislaw Brzezniak, Annie Millet. On the splitting method for some complex-valued quasilinear evolution equations. In Honour of Ali Süleyman Üstünel, Jun 2010, Paris, France. pp.57-90, ⟨10.1007/978-3-642-29982-7⟩. ⟨hal-00555063⟩