On the behaviour of a rumour process with random stifling

Environmental Modelling and Software

Volumn 26, Issue 4, 2011, Pages 517-522

  Lebensztayn, E ^a   Machado, F P ^a   Rodriguez P M ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

60F05; 60J27; 60K30; Limit theorems; Maki Thompson; Markov chain; Stochastic rumour

Indexed keywords

60F05; 60J27; 60K30; LIMIT THEOREM; MARKOV CHAIN; STOCHASTIC RUMOUR; THOMPSON;

ASYMPTOTIC ANALYSIS; MARKOV PROCESSES; POPULATION STATISTICS;

STOCHASTIC SYSTEMS;

LIMIT ANALYSIS; MARKOV CHAIN; POPULATION SIZE; STOCHASTICITY;

EID: 78650531263     PISSN: 13648152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.envsoft.2010.10.015     Document Type: Article

References (16)

1. Belen, S., 2008. The behaviour of stochastic rumours. Ph.D. thesis, School of Mathematical Sciences, University of Adelaide, Australia. Available at: http://hdl.handle.net/2440/49472.
2. Belen S., Pearce C.E.M. Rumours with random initial conditions. The Australian & New Zealand Industrial and Applied Mathematics Journal 2004, 45:393-400.
3. Carnal H. Calcul des probabilités et modélisation. Elemente der Mathematik 1994, 49(4):166-173.
4. Corless R.M., Gonnet G.H., Hare D.E.G., Jeffrey D.J., Knuth D.E. On the Lambert W function. Advances in Computational Mathematics 1996, 5(4):329-359.
5. Daley D.J., Gani J. Epidemic Modelling: An Introduction 1999, Cambridge University Press, Cambridge.
6. Daley D.J., Kendall D.G. Stochastic rumours. Journal of the Institute of Mathematics and Its Applications 1965, 1:42-55.
7. Dunstan R. The rumour process. Journal of Applied Probability 1982, 19(4):759-766.
8. Ethier S.N., Kurtz T.G. Markov Process: Characterization and Convergence. Wiley Series in Probability and Mathematical Statistics 1986, John Wiley & Sons Inc., New York.
9. Gani J. The Maki-Thompson rumour model: a detailed analysis. Environmental Modelling & Software 2000, 15:721-725.
10. Kurtz T.G., Lebensztayn E., Leichsenring A.R., Machado F.P. Limit theorems for an epidemic model on the complete graph. ALEA. Latin American Journal of Probability and Mathematical Statistics 2008, 4:45-55.
11. Lebensztayn E., Machado F.P., Rodríguez P.M. Limit theorems for a general stochastic rumour model Available at:. http://arxiv.org/abs/1003.4995.
12. Lefevre C., Picard P. Distribution of the final extent of a rumour process. Journal of Applied Probability 1994, 31(1):244-249.
13. Maki D.P., Thompson M. Mathematical Models and Applications 1973, Prentice-Hall, Englewood Cliffs.
14. Pearce C.E.M. The exact solution of the general stochastic rumour. Mathematical and Computer Modelling 2000, 31:289-298.
15. Sudbury A. The proportion of the population never hearing a rumour. Journal of Applied Probability 1985, 22(2):443-446.
16. Watson R. On the size of a rumour. Stochastic Processes and Their Applications 1988, 27:141-149.