Bayesian inference for generalised tempered stable Levy processes.

该项目的目标是基于Levy过程的离散时间观测和对这些方法的理论研究，开发出新的高效的Levy过程贝叶斯推理方法。特别地，对于广义回火稳定过程，我们计划使用非参数贝叶斯方法来估计回火函数。一个重要的任务是开发有效的MCMC算法，并证明相应的压缩率。还预计将实施拟议的方法，并将其应用于金融和保险数据。

The goal of the project is the development of new efficient methods of Bayesian inference for Levy processes based on their discrete-time observations and theoretical investigation of these methods. In particular, for the class of generalized tempered stable processes, we plan to estimate the tempering function using a nonparametric Bayesian approach. An important task is development of efficient MCMC algorithms and proof of the corresponding contraction rates. The implementation of proposed methods and their application to financial and insurance data is also foreseen.