On using the first difference in the Stein-Chen method

Annals of Applied Probability

Volumn 7, Issue 4, 1997, Pages 899-916

  Xia, Aihua ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Coupling; Immigration death process; Palm distributions; Stein Chen method

Indexed keywords

EID: 0031260677     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1043862417     Document Type: Article

References (19)

1. ARRATIA, R., GOLDSTEIN, L. and GORDON, L. (1989). Two moments suffice for Poisson approximations: the Chen-Stein method. Ann. Probab. 17 9-25.
2. BARBOUR, A. D. (1988). Stein's method and Poisson process convergence. J. Appl. Probab. 25A 175-184.
3. BARBOUR, A. D. and BROWN, T. C. (1992a). Stein's method and point process approximation. Stochastic Process. Appl. 43 9-31.
4. BARBOUR, A. D. and BROWN, T. C. (1992b). Stein-Chen method, point processes and compensators. Ann. Probab. 20 1504-1527.
5. BARBOUR, A. D., BROWN, T. C. and XIA, A. (1995). Point processes in time and Stein's method. Unpublished manuscript.
6. BARBOUR, A. D. and HALL, P. (1984). On the rate of Poisson convergence. Math. Proc. Cambridge Philos. Soc. 95 473-480.
7. BARBOUR, A. D., HOLST, L. and JANSON, S. (1992). Poisson Approximation. Oxford Univ. Press.
8. BARBOUR, A. D. and JENSEN, J. L. (1989). Local and tail approximations near the Poisson limit. Scared. J. Statist. 16 75-87.
9. BROWN, T. C. and GREIG, D. (1996). Poisson approximation for point processes via monotone couplings. Ann. Appl. Probab. 545-560.
10. BROWN, T. C. and XIA, A. (1995a). On metrics in point process approximation. Stochastics Stochastics Rep. 52 247-263.
11. BROWN, T. C. and XIA, A. (1995b). On Stein-Chen factors for Poisson approximation. Statist. Probab. Lett. 23 327-332.
12. CHEN, L. H. Y. (1975). Poisson approximation for dependent trials. Ann. Probab. 3 534-545.
13. DALEY, D. J. and VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York.
14. DEHEUVELS, P. and PFEIFER, D. (1986). A semigroup approach to Poisson approximation. Ann. Probab. 14 665-678.
15. DEHEUVELS, P. and PFEIFER, D. (1988). On a relationship between Uspensky's theorem and Poisson approximations. Ann. Inst. Statist. Math. 40 671-681.
16. KALLENBERG, O. (1983). Random Measures. Academic Press, New York.
17. KARR, A. F. (1986). Point Processes and Their Statistical Inference. Dekker, New York.
18. RACHEV, S. T. (1984). The Monge-Kantorovich mass transference problem and its stochastic applications. Theory Probab. Appl. 29 647-676.
19. XIA, A. (1997). On the rate of Poisson process approximation to a Bernoulli process. J. Appl. Probab. To appear.