DISTRIBUTION FUNCTION OF FIRST EXIT TIME FOR A COMPOUND POISSON PROCESS

Öz

In this study, the first exit time of a compound Poisson process with positive jumps and an upper horizontal boundary is considered. An explicit formula is derived for the distribution function of the first exit time associated with the compound Poisson process. By means of a proposed algorithm, some numerical examples and an application on traffic accidents are also given to illustrate the usage of the distribution function of the first exit time and proposed algorithm.

Anahtar Kelimeler

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BİRLEŞİK POISSON SÜRECİ İÇİN İLK AŞMA ZAMANININ DAĞILIM FONKSİYONU

Öz

Bu çalışmada, pozitif adımlı ve üst yatay sınırlı bir birleşik Poisson sürecinin ilk aşma zamanı göz önünde bulundurulmuş ve ilk aşma zamanının kesin formülüne ulaşılmıştır. İlk aşma zamanının dağılım fonksiyonunun ve önerilen algoritmanın uygulanabilirliğini göstermek için bazı sayısal örnekler ve trafik kazaları üzerine bir uygulama verilmiştir

Anahtar Kelimeler

• Birleşik poisson süreci, İlk aşma zamanı, Üst yatay sınır, Oracle veritabanı

Kaynakça

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