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math.NA2009★ 50 cited
Convergence of the stochastic Euler scheme for locally Lipschitz coefficients
Martin Hutzenthaler, Arnulf Jentzen
Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous…
math.NA2009★ 442 cited
Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden
The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation with globally Lipschitz continuous drift and diffusion coefficient. Rec…
math.NA2009★ 3 cited
Taylor expansions of solutions of stochastic partial differential equations
Arnulf Jentzen
The solutions of parabolic and hyperbolic stochastic partial differential equations (SPDEs) driven by an infinite dimensional Brownian motion, which is a martingale, are in general…