Abstract A subordinate diffusion is a Markovian jump-diffusion or pure jump process obtained by time changing a diffusion process with an independent Lévy or additive subordinator. This class of processes has found many applications in financial modeling. In this paper, we develop sufficient conditions and necessary conditions for the distributions of two subordinate diffusions to be equivalent, which are important for derivatives pricing and calibration. We obtain asymptotics for the jump intensity of a large class of subordinate diffusions near zero, which allow us to reduce these conditions to explicit restrictions on the model parameters that can be directly checked in applications. These asymptotics are also useful in detecting finiteness of the jump variation for these processes.

中文翻译：

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从属扩散的等效测量变化

摘要 从属扩散是一个马尔可夫跳跃扩散或纯跳跃过程，通过时间改变扩散过程与独立的 Lévy 或加性从属。此类流程已在金融建模中找到了许多应用。在本文中，我们开发了两个从属扩散的分布相等的充分条件和必要条件，这对于衍生品定价和校准很重要。我们获得了一大类接近零的从属扩散的跳跃强度的渐近线，这使我们能够将这些条件减少到对模型参数的明确限制，这些限制可以在应用程序中直接检查。这些渐近性也可用于检测这些过程的跳跃变化的有限性。