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Boundary functionals for the superposition of a random walk and a sequence of independent random variables
Author(s):
I.
I.
Ezhov;
V.
F.
Kadankov
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 75
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 75
(2007),
9-22.
MSC (2000):
Primary 60J05, 60J10;
Secondary 60J45
Posted:
January 23, 2008
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Additional information
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:
-
- 1.
- 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)
- 2.
- F. Spitzer, Principles of Random Walk, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1964. MR 0171290 (30:1521)
- 3.
- A. A. Borovkov, Stochastic Processes in Queueing Theory, ``Nauka'', Moscow, 1972; English transl., Springer-Verlag, New York-Berlin, 1976. MR 0315800 (47:4349)
- 4.
- 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)
- 5.
- 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
DOI:
10.1090/S0094-9000-07-00710-7
PII:
S 0094-9000(07)00710-7
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):
25/APR/2005
Posted:
January 23, 2008
Copyright of article:
Copyright
2007,
American Mathematical Society
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