Generalised hyperbolic (GH) processes are a class of stochastic processes that are used to model the dynamics of a wide range of complex systems that exhibit heavy-tailed behavior, including systems in finance, economics, biology, and physics. In this paper, we present novel simulation methods based on subordination with a generalised inverse Gaussian (GIG) process and using a generalised shot-noise representation that involves random thinning of infinite series of decreasing jump sizes. Compared with our previous work on GIG processes, we provide tighter bounds for the construction of rejection sampling ratios, leading to improved acceptance probabilities in simulation. Furthermore, we derive methods for the adaptive determination of the number of points required in the associated random series using concentration inequalities. Residual small jumps are then approximated using an appropriately scaled Brownian motion term with drift. Finally the rejection sampling steps are made significantly more computationally efficient through the use of squeezing functions based on lower and upper bounds on the L\'evy density. Experimental results are presented illustrating the strong performance under various parameter settings and comparing the marginal distribution of the GH paths with exact simulations of GH random variates. The new simulation methodology is made available to researchers through the publication of a Python code repository.

翻译：广义双曲线（GH）过程是一类用于模拟表现出重尾行为的复杂系统动态的随机过程，广泛应用于金融、经济学、生物学和物理学等领域。本文提出基于广义逆高斯（GIG）过程从属化及广义散粒噪声表示的新颖模拟方法，该方法通过随机稀疏化处理递减跳跃幅度的无穷级数来实现。相较于我们此前关于GIG过程的研究，本文为拒绝抽样比率的构造提供了更严格的上界，从而提升了模拟中的接受概率。此外，我们利用浓度不等式推导了相关随机序列所需点数的自适应确定方法，并使用带漂移项的适当缩放布朗运动项近似剩余小跳跃。通过基于莱维密度下界和上界的挤压函数，显著提高了拒绝抽样步骤的计算效率。实验结果表明，该方法在不同参数设置下均表现出优异性能，并将GH路径的边际分布与GH随机变量的精确模拟结果进行了比较。通过发布Python代码库，研究人员可获取这一新型模拟方法。