Boundary functionals for the superposition of a random walk and a sequence of independent random variables
Authors:
I. I. Ezhov and V. F. Kadankov
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 75 (2007), 9-22
MSC (2000):
Primary 60J05, 60J10; Secondary 60J45
DOI:
https://doi.org/10.1090/S0094-9000-07-00710-7
Published electronically:
January 23, 2008
MathSciNet review:
2321177
Full-text PDF Free Access
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Abstract: For the superposition of a random walk and a sequence of independent random variables, we obtain the moment generating functions of the joint distribution of the first passage time and overshoot over a level, and those of the joint distribution of the first exit time from an interval and the value of the superposition at the exit time.
References
- E. A. Pečerskiĭ and B. A. Rogozin, The combined distributions of the random variables connected with the fluctuations of a process with independent increments, Teor. Verojatnost. i Primenen. 14 (1969), 431–444 (Russian, with English summary). MR 0260005
- Frank Spitzer, Principles of random walk, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1964. MR 0171290
- A. A. Borovkov, Veroyatnostnye protsessy v teorii massovogo obsluzhivaniya, Izdat. “Nauka”, Moscow, 1972 (Russian). MR 0315800
- V. F. Kadankov and T. V. Kadankova, On the distribution of the first exit time from an interval and the value of the overjump across a boundary for processes with independent increments and random walks, Ukraïn. Mat. Zh. 57 (2005), no. 10, 1359–1384 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 57 (2005), no. 10, 1590–1620. MR 2219768, DOI https://doi.org/10.1007/s11253-006-0016-6
- I. G. Petrovskiĭ, Lektsii po teorii integral′nykh uravneniĭ, Izdat. “Nauka”, Moscow, 1965 (Russian). Third edition, revised. MR 0352904
References
- E. A. Pecherskiĭ and B. A. Rogozin, The joint distributions of random variables associated to fluctuations of a process with independent increments, Teor. Veroyatnost. Primenen. 14 (1969), no. 3, 431–444; English transl. in Theor. Probab. Appl. 14 (1969), no. 3, 410–423. MR 0260005 (41:4634)
- F. Spitzer, Principles of Random Walk, D. Van Nostrand Co., Inc., Princeton, N.J.–Toronto–London, 1964. MR 0171290 (30:1521)
- A. A. Borovkov, Stochastic Processes in Queueing Theory, “Nauka”, Moscow, 1972; English transl., Springer-Verlag, New York–Berlin, 1976. MR 0315800 (47:4349)
- V. F. Kadankov and T. V. Kadankova, On the distribution of the first exit time from an interval and the value of the overjump across a boundary for processes with independent increments and random walks, Ukrain. Mat. Zh. 57 (2005), no. 10, 1359–1384; English transl. in Ukrainian Math. J. 57 (2005), no. 10, 1590–1620. MR 2219768 (2007b:60119)
- I. G. Petrovskiĭ, Lectures on the Theory of Integral Equations, “Nauka”, Moscow, 1965; English transl., Graylock Press, Rochester, New York, 1957. MR 0352904 (50:5390)
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Additional Information
I. I. Ezhov
Affiliation:
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka Street, 01601, Kyiv, Ukraine
V. F. Kadankov
Affiliation:
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka Street, 01601, Kyiv, Ukraine
Email:
kadankov@voliacable.com
Keywords:
Boundary functionals,
first exit time from an interval for a random walk,
the superposition of a random walk and a sequence of independent random variables
Received by editor(s):
April 25, 2005
Published electronically:
January 23, 2008
Article copyright:
© Copyright 2007
American Mathematical Society
