Grigoriu M
Cornell University, Ithaca, New York 14853-3501, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026704. doi: 10.1103/PhysRevE.80.026704. Epub 2009 Aug 21.
A fixed time step method is developed for integrating stochastic differential equations (SDE's) with Poisson white noise (PWN) and Lévy white noise (LWN). The method for integrating SDE's with PWN has the same structure as that proposed by Kim [Phys. Rev. E 76, 011109 (2007)], but is established by using different arguments. The integration of SDE's with LWN is based on a representation of Lévy processes by sums of scaled Brownian motions and compound Poisson processes. It is shown that the numerical solutions of SDE's with PWN and LWN converge weakly to the exact solutions of these equations, so that they can be used to estimate not only marginal properties but also distributions of functionals of the exact solutions. Numerical examples are used to demonstrate the applications and the accuracy of the proposed integration algorithms.
开发了一种固定时间步长方法，用于对带有泊松白噪声（PWN）和列维白噪声（LWN）的随机微分方程（SDE）进行积分。对带有PWN的SDE进行积分的方法与Kim [《物理评论E》76, 011109 (2007)] 提出的方法具有相同的结构，但基于不同的论证建立。对带有LWN的SDE进行积分是基于用缩放布朗运动和复合泊松过程的和来表示列维过程。结果表明，带有PWN和LWN的SDE的数值解弱收敛于这些方程的精确解，因此它们不仅可用于估计精确解的边际性质，还可用于估计精确解的泛函分布。通过数值例子展示了所提出的积分算法的应用和准确性。
