Abstract
For given two standard processes with no positive jumps, we construct, using excursion theory, a Markov process whose positive and negative motions have the same law as the two processes. The resulting process is a generalization of Kyprianou–Loeffen’s refracted Lévy processes. We discuss approximation problem for our refracted processes coming from Lévy processes by removing small jumps and taking the limit as the removal level tends to zero. We also discuss conditions for refracted processes to have dual processes.
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Acknowledgments
I would like to express my deepest gratitude to Professor Víctor Rivero and my supervisor Professor Kouji Yano for comments and improvements. Especially, Professor Kouji Yano gave me a lot of advice. The author was supported by JSPS-MAEDI Sakura program grant no. 16932157 and JSPS KAKENHI grant no. JP18J12680.
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Noba, K. Approximation and Duality Problems of Refracted Processes. Potential Anal 53, 591–612 (2020). https://doi.org/10.1007/s11118-019-09779-7
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DOI: https://doi.org/10.1007/s11118-019-09779-7