TITLE

# THE INTEGRAL LIMIT THEOREM IN THE FIRST PASSAGE PROBLEM FOR SUMS OF INDEPENDENT NONNEGATIVE LATTICE VARIABLES

AUTHOR(S)
Virchenko, Yuri P.; Yastrubenko, M. I.
PUB. DATE
January 2006
SOURCE
Abstract & Applied Analysis;2006, p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The integral limit theorem as to the probability distribution of the random number ?m of summands in the sum âˆ‘k=1?m Î¾k is proved. Here, Î¾1,Î¾2,â€¦ are some nonnegative, mutually independent, lattice random variables being equally distributed and ?m is defined by the condition that the sum value exceeds at the first time the given level m âˆŠ â„• when the number of terms is equal to ?m.
ACCESSION #
24081219

## Related Articles

• A GUE central limit theorem and universality of directed first andlast passage site percolation. Baik, Jinho; Suidan, Toufic M. // IMRN: International Mathematics Research Notices;2005, Vol. 2005 Issue 6, p325

We prove a GUE central limit theorem for random variables with finite fourth moment. We apply this theorem to prove that the directed first and last passage percolation problems in thin rectangles exhibit universal fluctuations given by the Tracy-Widom law.

• Some asymptotic results on extremes of incomplete samples. Tan, Zhongquan; Wang, Yuebao // Extremes;Sep2012, Vol. 15 Issue 3, p319

Let X, X, â‹¯ be a sequence of independent and identically distributed random variables and M = max { X, X, â‹¯ , X}. Suppose that some of the random variables X, X, â‹¯ , X can be observed and denote by \$\widetilde{M}_{n}\$ the maximum of the observed random variables from the set {...

• Quantum Algorithm for Modified Roulette Problem by Central Limit Theorem. Fujimura, Toru // Global Journal of Pure & Applied Mathematics;2012, Vol. 8 Issue 5, p541

A quantum algorithm for a modified roulette problem by the central limit theorem and its example are reported. When a random variable Vi [1 â‰¤ i = â‰¤ n. i and n are integers.] becomes ms [1 â‰¤ s â‰¤ t. ms, s and t are integers.] as each probability ks/K ... = ks and K are...

• Limit behaviour of sample modes for large number of independent random variables. Yosh, Harry // Azerbaijan Journal of Mathematics;Jan2012, Vol. 2 Issue 1, p107

Although the estimators of mode on finite independent random variables are widely used in various engineering fields, the feature regarding limit behaviour of sample modes for large number of independent random variables is not known except some special cases. Here we discuss the methodology for...

• On a theorem of V. N. Sudakov on typical distributions. Bobkov, S. G. // Journal of Mathematical Sciences;Jun2010, Vol. 167 Issue 4, p464

The rate of approximation with respect to the Kantorovichï¿½Rubinstein distance is considered in a theorem of V. N. Sudakov on typical distributions. Bibliography: 18 titles.

• Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of attraction of the normal law. Rozovsky, L. // Journal of Mathematical Sciences;May2005, Vol. 127 Issue 1, p1767

We investigate some aspects of asymptotic behavior of the probabilitiesP(Sn = a bn), where Sn is a sum of n independent random variables with common distribution function from the domain of attraction of the normal law, a is a positive number, and bn tends to infinity. In particular, necessary...

• A CENTRAL LIMIT THEOREM FOR STRONG NEAR-EPOCH DEPENDENT RANDOM VARIABLES. Lin Zhengyan; Qiu Jin // Chinese Annals of Mathematics;Apr2004, Vol. 25 Issue 2, p263

In this paper, a central limit theorem for strong near-epoch dependent sequences of random variables introduced in [9] is showed. Under the same moments condition, the authors essentially weaken the "size" requirement mentioned in other papers about near epoch dependence.

• Limit theorems for a recursive maximum process with location-dependent periodic intensity-parameter. Franke, Brice // Extremes;Mar2011, Vol. 14 Issue 1, p127

We investigate the recursive sequence Z: = max { Z, Î»( Z) X} where X is a sequence of iid random variables with exponential distributions and Î» is a periodic positive bounded measurable function. We prove that the CÃ©saro mean of the sequence Î»( Z) converges toward the essential...

• Quantum Algorithm for Modified Dice Problem by Central Limit Theorem. Fujimura, Toru // Global Journal of Pure & Applied Mathematics;2012, Vol. 8 Issue 4, p471

A quantum algorithm for a modified dice problem by the central limit theorem and its example are reported. When a random variable Vi[1â‰¤ i â‰¤ n. i and n are integers.] becomes 1,2, 3,4,5 and 6 as each probability 1/6, one example in orders that reach at a value is obtained. A...

Share