论文标题
拖网过程和范围字段的仿真方法和错误分析
Simulation methods and error analysis for trawl processes and ambit fields
论文作者
论文摘要
拖网过程是连续的，固定的和无限分开的过程，可以描述数据中广泛的串行相关模式。在本文中，我们引入了具有单调拖网函数的拖网过程的新仿真算法，并建立了其误差界限和收敛属性。我们广泛分析了这些算法的计算复杂性和实际实现，并讨论了哪种算法根据莱维的类型使用。我们将上述方法扩展到对内核加权，波动性调制拖网过程的模拟，并为横向场开发新的仿真算法。最后，我们讨论了先前在文献中描述的模拟方案如何与我们的方法结合使用，以减少计算成本。
Trawl processes are continuous-time, stationary and infinitely divisible processes which can describe a wide range of possible serial correlation patterns in data. In this paper, we introduce new simulation algorithms for trawl processes with monotonic trawl functions and establish their error bounds and convergence properties. We extensively analyse the computational complexity and practical implementation of these algorithms and discuss which one to use depending on the type of Lévy basis. We extend the above methodology to the simulation of kernel-weighted, volatility modulated trawl processes and develop a new simulation algorithm for ambit fields. Finally, we discuss how simulation schemes previously described in the literature can be combined with our methods for decreased computational cost.
