کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4613967 | 1339276 | 2016 | 26 صفحه PDF | دانلود رایگان |
We consider an extended birth–death–immigration process defined on a lattice formed by the integers of d semiaxes joined at the origin. When the process reaches the origin, then it may jump toward any semiaxis with the same rate. The dynamics on each ray evolves according to a one-dimensional linear birth–death process with immigration. We investigate the transient and asymptotic behavior of the process via its probability generating function. The stationary distribution, when existing, is a zero-modified negative binomial distribution. We also study a diffusive approximation of the process, which involves a diffusion process with linear drift and infinitesimal variance on each ray. It possesses a gamma-type transient density admitting a stationary limit. As a byproduct of our study, we obtain a closed form of the number of permutations with a fixed number of components, and a new series form of the polylogarithm function expressed in terms of the Gauss hypergeometric function.
Journal: Journal of Mathematical Analysis and Applications - Volume 442, Issue 1, 1 October 2016, Pages 291–316