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Exit time functionals for integer-valued Poisson processes


Author: D. V. Gusak
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal: Theor. Probability and Math. Statist. 68 (2004), 27-39
MSC (2000): Primary 60G50, 60J70
DOI: https://doi.org/10.1090/S0094-9000-04-00603-9
Published electronically: June 10, 2004
MathSciNet review: 2000392
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Abstract: The joint distribution of all exit time functionals is studied in this paper for a fixed level $x$ and integer-valued compound Poisson processes. An exact formula for the distributions of these functionals is obtained in the case of semicontinuous processes. Limit relations are obtained for the distributions of the exit time functionals for $x=0$ or as $x\to\infty$.


References [Enhancements On Off] (What's this?)

  • 1. D. V. Gusak, On the joint distribution of the first exit time and exit value for homogeneous processes with independent increments, Teor. Veroyatnost. i Primenen. 14 (1969), no. 1, 15-23; English transl. in Theor. Probab. Appl. 14 (1970), no. 1. MR 39:6395
  • 2. -, Distribution of overjump functionals of a homogeneous process with independent increments, Ukrain. Mat. Zh. 54 (2002), no. 3, 303-322; English transl., Ukrain. Math. J. 54 (2003), no. 3, 371-397. MR 2003j:60067
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Additional Information

D. V. Gusak
Affiliation: Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka Street 3, Kyiv 01601, Ukraine
Email: random@imath.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-04-00603-9
Received by editor(s): February 18, 2002
Published electronically: June 10, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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