Selahattin Maden

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

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.

Anahtar Kelimeler:

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

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,

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