On stationary renewal reward processes where most rewards are zero

Probability Theory and Related Fields

Volumn 117, Issue 2, 2000, Pages 145-161

  Erhardsson, Torkel ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Accumulated reward; Compound Poisson approximation; Coupling; Error bound; Palm process; Stationary renewal reward process; Stein's method

Indexed keywords

EID: 0034372148     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050001     Document Type: Article

References (18)

1. Aldous, D.: Probability approximations via the Poisson clumping heuristic, Springer, New York, 1989
2. Asmussen, S.: Applied probability and queues, Wiley, Chichester, 1987
3. Barbour, A.D., Brown, T.C.: The Stein-Chen method, point processes and compensators, Ann. Probab. 20, 1504-1527 (1992a)
4. Barbour, A.D., Brown, T.C.: Stein's method and point process approximation, Stochastic Process. Appl. 43, 9-31 (1992b)
5. Barbour, A.D., Chen, L.H.Y., Loh, W.-L.: Compound Poisson approximation for non-negative random variables via Stein's method, Ann. Probab. 20, 1843-1866 (1992)
6. Barbour, A.D., Holst, L., Janson, S.: Poisson approximation, Oxford University Press, 1992
7. Barbour, A.D., Utev, S.: Solving the Stein equation in compound Poisson approximation, Adv. in Appl. Probab. 30, 449-475 (1998)
8. Barbour, A.D., Utev, S.: Compound Poisson approximation in total variation, Stochastic Process. Appl. 82, 89-125 (1999)
9. Brown, T.C.: Some Poisson approximations using compensators, Ann. Probab. 11, 726-744 (1983)
10. Daley, D.J., Vere-Jones, D.: An introduction to the theory of point processes, Springer, New York, 1988
11. Erhardsson, T.: Compound Poisson approximation for Markov chains using Stein's method, Ann. Probab. 27, 565-596 (1999)
12. Kabanov, Yu.M., Liptser, R.Sh.: On convergence in variation of the distributions of multivariate point processes, Z. Wahrsch. Verw. Gebiete 31, 235-253 (1983)
13. Kallenberg, O.: Limits of compound and thinned point processes, J. Appl. Probab. 8, 269-278 (1975)
14. Kallenberg, O.: Random measures, 3rd ed. Akademie-Verlag, Berlin, 1983
15. Lorden, G.: On excess over the boundary, Ann. Math. Statist. 41, 520-527 (1970)
16. Rényi, A.: A characterization of Poisson processes, (Hungarian; English and Russian summaries.) Magyar Tud. Akad. Mat. Kutató Int. Közl. 1, 519-527 (1956). Translation in: Turán, P., Ed.: Selected papers of Alfréd Rényi, Vol. 1, 622-628. Akadémiai Kiadó, Budapest, 1976
17. Rényi, A.: A characterization of Poisson processes, (Hungarian; English and Russian summaries.) Magyar Tud. Akad. Mat. Kutató Int. Közl. 1, 519-527 (1956). Translation in: Turán, P., Ed.: Selected papers of Alfréd Rényi, Vol. 1, 622-628. Akadémiai Kiadó, Budapest, 1976
18. Rolski, T.: Stationary random processes associated with point processes, Lecture notes in statistics, Vol. 5. Springer, New York, 1981