Stationarity properties of neural networks

Journal of Applied Probability

Volumn 35, Issue 4, 1998, Pages 783-794

  Asmussen, Søren ^a   Turova, Tatyana S ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

Inhibition; Ladder height distribution; Palm theory; Path decomposition; Queuing theory; Random walk; Renewal process; Waiting time distribution

Indexed keywords

EID: 0032250909     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200016491     Document Type: Article

References (15)

1. ALSMEYER, G. (1996). Superimposed renewal processes: a Markov renewal approach. Stoch. Proc. Appl. 61, 311-322.
2. ASMUSSEN, S. (1987). Applied Probability and Queues, Wiley, Chichester.
3. BACCELLI, F. AND BREMAUD, P. (1994). Elements of Queuing Theory. Palm-Martingale Calculus and Stochastic Recursions, Springer, Berlin.
4. BACCELLI, F. AND MAKOWSKI, A. M. (1989). Dynamic, transient and stationary behavior of the M/G/1 queue via martingales. Ann. Prob. 17, 1691-1699.
5. COTTRELL, M. (1992). Mathematical analysis of a neural network with inhibitory coupling. Stoch. Proc. Appl. 40, 103-126.
6. FRICKER, C., ROBERT, P., SAADA, E. AND TIBI, D. (1994). Analysis of some networks with interaction. Ann. Appl. Prob. 4, 1112-1128.
7. KARPELEVICH, F., MALYSHEV, V. A. AND RYBKO, A. N. (1995). Stochastic evolution of neural networks. Markov Proc. Rel. Fields 1, 141-161.
8. KRYUKOV, V. I., BORISYUK, G. N., BORISYUK, R. M, KIRILLOV, A. B. AND KOVALENKO, YE. I. (1990). Metastable and unstable states in the brain. In Stochastic Cellular Systems: Ergodicity, Memory, Morphogenesis, ed. R. L. Dobrushin, V. I. Kryukov and A. L. Toom. Manchester University Press, pp. 226-357.
9. PITMAN, J. W. (1975). An identity for stopping times of a Markov chain. In Studies in Probability and Statistics, ed. E. J. Williams, North-Holland, Amsterdam.
10. ROSENKRANTZ, W. A. (1983). Calculation of the Laplace transform of the length of the busy period of the M/G/1 queue via martingales. Ann. Prob. 11, 817-818.
11. SIGMAN, K. (1994). Stationary Marked Point Processes: An Intuitive Approach, Chapman and Hall, New York.
12. TUROVA, T. S. (1994). Analysis of some stochastic neural models. In Aportaciones Matemáticas, Serie Notas de Investigación 11. Sociedad Matemática Mexicana, Mexico, pp. 157-169.
13. TUROVA, T. S. (1996). Stochastic dynamics of a neural network with inhibitory and excitatory connections. BioSystems 40, 197-202.
14. TUROVA, T. S. (1996). Analysis of a biologically plausible neural network via an hourglass model. Markov Proc. Rel. Fields 2, 487-510.
15. TUROVA, T. S., MOMMAERTS, W. AND VAN DER MEULEN, E. C. (1994). Synchronization of firing times in a stochastic neural network model with excitatory connections. Stoch. Proc. Appl. 50, 173-186.