Integral Limit Theorems for Nonlinear Boundary Crossing Time by Sums of Independent Variables

2006 ◽  
Vol 50 (1) ◽  
pp. 165-168 ◽  
Author(s):  
F. G. Ragimov
Keyword(s):  
Limit Theorems ◽  
Nonlinear Boundary ◽  
Boundary Crossing ◽  
Integral Limit ◽  
Independent Variables ◽  
Crossing Time

Boundary crossing for moving sums

1988 ◽  
Vol 25 (1) ◽  
pp. 81-88 ◽  
Author(s):  
J. Glaz ◽  
B. Johnson
Keyword(s):  
Standard Deviation ◽  
Random Variables ◽  
Boundary Crossing ◽  
Time Approximation ◽  
Crossing Time ◽  
Moving Sum

Let Xi, i ≧ 1, be a sequence of independent N(0, 1) random variables and Sj,m = Xj + · ·· + Xj+m–1, the jth moving sum. Let τ m = inf{j ≧ 1 : Sj,m > a} + m – 1, the boundary crossing time. Approximation in the spirit of Glaz and Johnson (1984), (1986) and Samuel-Cahn (1983) are given for Pr(τm > n), E(τ m), and σ (τ m),the standard deviation of τm.

Some integral limit theorems for additive functions

1977 ◽  
Vol 16 (4) ◽  
pp. 564-573
Author(s):  
B. V. Levin ◽  
N. M. Timofeev
Keyword(s):  
Limit Theorems ◽  
Additive Functions ◽  
Integral Limit
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