Step size control for the uniform approximation of systems of stochastic differential equations with additive noise

摘要: We analyze the pathwise approximation for systems of stochastic differential equations.The distance between solution and its is measured globally on unit interval in the $L_{\infty}$-norm, we study expectation this distance. For systems with additive noise obtain sharp lower upper bounds minimal error class arbitrary methods which use discrete observations a Brownian path. The optimal order achieved by an Euler scheme adaptive step-size control. illustrate superiority adaptive method compared to equidistant discretization a simulation experiment.