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Theory of Probability and Mathematical Statistics

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A simplified version of Spitzer's formula for semicontinuous and almost semicontinuous processes

Author: D. V. Gusak
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 61-71
MSC (2000): Primary 60G50; Secondary 60K10
Published electronically: January 11, 2013
MathSciNet review: 2933703
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Abstract: Let $ \{\xi (t), \zeta (0)=0, t\geq 0\}$ be a process with stationary independent increments. We establish simplified versions of relations for spectral functions in Spitzer's formulas in terms of the exponential function whose index is determined by the corresponding root of Lundberg's equation for the case where $ \xi (t)$ is a semicontinuous or almost semicontinuous process.

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Additional Information

D. V. Gusak
Affiliation: Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivs’ka Street, 3, 252601 Kyiv–4, Ukraine

Keywords: Semicontinuous and almost semicontinuous processes with independent increments, Spitzer’s formula, Lundberg’s equation, Spitzer’s spectral functions
Received by editor(s): December 10, 2010
Published electronically: January 11, 2013
Article copyright: © Copyright 2013 American Mathematical Society

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