İki Tutan Bariyerli Yarı-Markovian Rastgele Yürüyüş Sürecinin Bir Sinir Fonksiyonalinin Dağılımı Hakkında

Year 2017, Volume: 7 Issue: 2, 319 - 329, 15.12.2017

Selahattin Maden

Abstract

Bu çalışmada, rastgele yürüyüşün
(1 ;1 )
 
L
Laplace dağılımına sahip olması durumunda, sıfır ve
 ( 0 )  
seviyelerinde tutan bariyerlere sahip bir yarı-Markovian rastgele yürüyüş süreci ve
bu sürecin sıfır seviyesindeki tutan bariyere ilk kez düşme anı, ( ), 0

matematiksel olarak
kurulmuştur. Daha sonra
0

rastgele değişkeninin Laplace dönüşümünün açık bir ifadesi
verilmiştir. Ayrıca bu Laplace dönüşümünü kullanarak,
0

rastgele değişkeninin beklenen değer
ve varyansı için basit formüller elde edilmiştir. 

Keywords

Yarı-Markovian rastgele yürüyüş süreci, Laplace dağılımı, Tutan bariyer, Beklenen değer, Varyans, Laplace dönüşümü

On the Distribution of a Boundary Functional of the Semi-Markovian Random Walk Process with Two Delaying Barriers

Abstract

In this study, a process of semi-Markovian random walk with delaying barriers at
0  and
  levels (
  0
) and first falling moment of the process into the delaying barrier at zerolevel,
( )
0
 , are mathematically constructed, in this case when the random walk happens
according to the Laplace’s distribution
(1 ;1 )
 
L . Then it is given an explicit expression of the
Laplace transformation of the distribution of random variable
0
 . Also the simple formulas for
expectation and variance of random variable
0

are obtained by the means of this Laplace
transformation.

Keywords

Semi-Markovian random walk process, Laplace distribution, delaying barrier, expected value, variance, Laplace transformation

References

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