论文标题
在随机Magnus的扩张及其在SPDES上的应用
On the stochastic Magnus expansion and its application to SPDEs
论文作者
论文摘要
我们为随机微分方程（SDE）的线性系统的Magnus扩展的随机版本得出。关于相关文献的主要新颖性是，我们在ITô意义上考虑了SDE，并具有逐渐可测量的系数，因此无法提供显式的Itô-Stratonovich转换。我们证明了马格努斯膨胀到停止时间τ的收敛性，并提供了t的累积分布函数的新型渐近估计。作为一种应用，我们提出了一种基于空间离散化和随机马格努斯扩张的应用的随机部分微分方程（SPDE）的数值解的新方法。该方法的一个显着特征是它是完全可行的。我们还提出了数值测试，以评估数值方案的准确性。
We derive the stochastic version of the Magnus expansion for linear systems of stochastic differential equations (SDEs). The main novelty with respect to the related literature is that we consider SDEs in the Itô sense, with progressively measurable coefficients, for which an explicit Itô-Stratonovich conversion is not available. We prove convergence of the Magnus expansion up to a stopping time τ and provide a novel asymptotic estimate of the cumulative distribution function of t. As an application, we propose a new method for the numerical solution of stochastic partial differential equations (SPDEs) based on spatial discretization and application of the stochastic Magnus expansion. A notable feature of the method is that it is fully parallelizable. We also present numerical tests in order to asses the accuracy of the numerical schemes.
