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Weak convergence of censored and reflected stable processes

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  • Kim, Panki

Abstract

It is shown that if a sequence of open n-sets Dk increases to an open n-set D then reflected stable processes in Dk converge weakly to the reflected stable process in D for every starting point x in D. The same result holds for censored [alpha]-stable processes for every x in D if D and Dk satisfy the uniform Hardy inequality. Using the method in the proof of the above results, we also prove the weak convergence of reflected Brownian motions in unbounded domains.

Suggested Citation

  • Kim, Panki, 2006. "Weak convergence of censored and reflected stable processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1792-1814, December.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:12:p:1792-1814
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    References listed on IDEAS

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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    2. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    3. Kim, Panki, 2003. "Fatou's Theorem for censored stable processes," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 63-92, November.
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    2. Li, Liping & Li, Xiaodan, 2020. "Dirichlet forms and polymer models based on stable processes," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 5940-5972.
    3. Alonso Ruiz, Patricia, 2021. "Heat kernel analysis on diamond fractals," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 51-72.

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