We propose a class of polynomial birth-death point processes (abbreviated to PBDP) , where Z is a polynomial birth-death random variable defined in [T.C. Brown, A. Xia, Stein's method and birth-death processes, Ann. Probab. 29 (2001) 1373-1403], Ui's are independent and identically distributed...

The Poisson process has the well-known Poisson count property: the count of points in any subset of the carrier space has a Poisson distribution. To specify the complete distribution of a point process it is necessary and sufficient to specify all of the joint distributions of the counts of...

We present a new approximation theorem for estimating the error in approximating the whole distribution of a finite-point process by a suitable Poisson process. The metric used for this purpose regards the distributions as close if there are couplings of the processes with the expected average...

This paper gives an upper bound for a Wasserstein distance between the distributions of a partial sum process of a Markov chain and a Poisson process on the positive half line in terms of the transition probabilities and the stationary distribution of the Markov chain. The argument is based on...

The Stein-Chen method for the estimation of upper bounds of the distance of the whole distribution of a point process from that of a Poisson process was investigated in Barbour and Brown (1992). A feature of the Stein-Chen approximation for random variables is the existence of "magic" factors...