Fatou's Theorem for censored stable processes

Panki Kim

Stochastic Processes and their Applications, 2003, vol. 108, issue 1, 63-92

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.

Keywords: Green; function; Censored; stable; process; Fatou's; Theorem; Martin; kernel; Martin; boundary; Harmonic; function; Feynman-Kac; transforms; Martin; representation (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (1)

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