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Fatou's Theorem for censored stable processes

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  • Kim, Panki

Abstract

We give a proof of Fatou's Theorem for censored [alpha]-stable processes in a bounded C1,1 open set D where [alpha][set membership, variant](1,2). As an application of Fatou's Theorem, we show that the harmonic measure for such censored [alpha]-stable process is mutually absolutely continuous with respect to the surface measure of [not partial differential]D. Fatou's Theorem is also established for operators obtained from the generator of the censored [alpha]-stable process through non-local Feynman-Kac transforms. Fatou's Theorem for censored relativistic stable processes is also true as a consequence.

Suggested Citation

  • Kim, Panki, 2003. "Fatou's Theorem for censored stable processes," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 63-92, November.
    • Handle: RePEc:eee:spapps:v:108:y:2003:i:1:p:63-92
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    Cited by:

    1. Kim, Panki, 2006. "Weak convergence of censored and reflected stable processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1792-1814, December.

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