On calculation of moments of ladder heights |
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Authors: | A K Aleškevičienė |
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Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania |
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Abstract: | Let X,X
1,X
2, … be independent identically distributed random variables, F(x) = P{X < x}, S
0 = 0, and S
n
=Σ
i=1
n
X
i
. We consider the random variables, ladder heights Z
+ and Z
− that are respectively the first positive sum and the first negative sum in the random walk {S
n
}, n = 0, 1, 2, …. We calculate the first three (four in the case EX = 0) moments of random variables Z
+ and Z
− in the qualitatively different cases EX > 0, EX < 0, and EX = 0.
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Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 2, pp. 159–179, April–June, 2006. |
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Keywords: | random walk ladder heights moments of ladder heights |
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