Rejection Sampling for Tempered Levy Processes

TL;DR

This paper introduces a rejection sampling method for tempered Levy processes, extending tempering techniques to broader classes and demonstrating its effectiveness through simulations.

Contribution

It generalizes tempering stable Levy processes to wider Levy classes and develops a rejection sampling algorithm for these processes.

Findings

Effective sampling algorithm demonstrated

Decomposition into tempered process and jump process

Simulation results illustrate performance

Abstract

We extend the idea of tempering stable Levy processes to tempering more general classes of Levy processes. We show that the original process can be decomposed into the sum of the tempered process and an independent point process of large jumps. We then use this to set up a rejection sampling algorithm for sampling from the tempered process. A small scale simulation study is given to help understand the performance of this algorithm.