We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Lévy white noises. A recent paper showed that these processes are limits in law of generalized compound-Poisson processes. Based on this result, we derive an off-the-grid algorithm that generates arbitrarily close approximations of the target process. Our method relies on a B-spline representation of generalized compound-Poisson processes. We illustrate numerically the validity of our approach.

中文翻译：

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使用匹配样条生成稀疏随机过程

我们提供了一种算法来生成稀疏随机过程的轨迹，这些过程是由 Lévy 白噪声驱动的线性常微分方程的解。最近的一篇论文表明，这些过程是广义复合泊松过程定律的极限。基于这个结果，我们推导出一种离网算法，该算法生成目标进程的任意接近的近似值。我们的方法依赖于广义复合泊松过程的 B 样条表示。我们用数字说明了我们方法的有效性。