Lévy Approximation of Increment Processes with Markov Switching

Abstract

We study weak convergence of increment processes with embedded Markov chain switching in a series scheme. The limit process is a Lévy process where the jump part is a compound Poisson process. A result concerning the rate of convergence is also given. This study is motivated by risk theory and its applications.

Keywords:

• Increment process
• Lévy process
• Weak convergence
• Compound Poisson process
• Risk process
• Markov additive process
• 60F17
• 60J25
• 60J75
• 60K37

Acknowledgements

The authors are grateful to an anonymous referee for his useful comments that improved the presentation of this paper.