Regularitaetseigeschaften und approximationen fuer stochastische gewoehnliche und partielle Differentialgleichungen mit nicht global Lipschitz-stetigen Nichtlinearitaeten (SDE)

Grunddaten zu diesem Projekt

Beschreibung

A number of stochastic ordinary and partial differential equations from the literature (such as, for example, the Heston and the 3/2-model from financial engineering, (overdamped) Langevin-type equations from molecular dynamics, stochastic spatially extended FitzHugh-Nagumo systems from neurobiology, stochastic Navier-Stokes equations, Cahn-Hilliard-Cook equations) contain non-globally Lipschitz continuous nonlinearities in their drift or diffusion coefficients. A central aim of this project is to investigate regularity properties with respect to the initial values of such stochastic differential equations in a systematic way. A further goal of this project is to analyze the regularity of solutions of the deterministic Kolmogorov partial dfferential equations associated to such stochastic differential equations. Another aim of this project is to analyze weak and strongconvergence and convergence rates of numerical approximations for such stochastic differential equations.