A note on the characteristics of Poisson processes
Tóm tắt
In this note two characteristic theorems of Poisson processes are given. If {N(t);t≧0} is a renewal process,U
t
,V
t
are, respectively, the time since the last renewal and the time to the next renewal att, Z
t
=U
t
+V
t
, then a Poisson process can be characterized by the limiting independene of the joint distribution of (U
t
,V
t
) whent→∞, orEZ
t
, or the distribution ofZ
t
.
Tài liệu tham khảo
Chung, K. L., The Poisson Process a a Renewal Process.Periodica Mathematica Humgar.,2 (1972), 41–48.
Çinlar, E., and Jagers, P., Introduction to Stochastic Processes. Prentice-Hall Inc., 1975.