Analytic expansions of max-plus Lyapunov exponents

Annals of Applied Probability

Volumn 10, Issue 3, 2000, Pages 779-827

  Baccelli, François ^a   Hong, Dohy ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

(Max, plus) semiring; Analyticity; Lyapunov exponents; Network modeling; Renovating events; Stationary state variables; Stochastic Petri nets; Strong coupling; Taylor series; Vectorial recurrence relation

Indexed keywords

EID: 0034346714     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1019487510     Document Type: Article

References (17)

1. BACCELLI, F., COHEN, G., OLSDER, G. J. and QUADRAT, J. P. (1992). Synchronization and Linearity. Wiley, New York.
2. BACCELLI, F., HASENFUSS, S. and SCHMIDT, V. (1999). Differentiability of Poisson driven stochastic systems. Stochastic Process. Appl. 81 271-299.
3. BACCELLI, F. and MAIRESSE, J. (1998). Erodic theorems for stochastic operators and discrete event networks. In Idempotency (J. Gunawardena, ed.) 171-208. Cambridge Univ. Press.
4. BOROVKOV, A. and FOSS, S. (1992). Stochastically recursive sequences and their generalizations. Siberian Adv. Math. 2 16-81.
5. BRILMAN, M. and VINCENT, J. M. (1997). Dynamics of synchronized parallel systems. Stochastic Models 3 605-618.
6. COCHET-TERRASSON, J., GAUBERT, S. and GUNAWARDENA, J. (1999). Dynamics of min-max functions. Dynamic Stability Systems 14 407-433.
7. COHEN, J. E. (1988). Subadditivity, generalized product of random matrices and operations research. SIAM Rev. 30 69-86.
8. GAUBERT, S. (1996). On the Burnside problem for semigroups of matrices in the (max, +) algebra. Semigroup Forum 52 271-292.
9. GAUBERT, S. and MAIRESSE, J. (1998). Task resource models and (max, +) automata. In Idempotency (J. Gunawardena, ed.) 133-144. Cambridge Univ. Press.
10. GUNAWARDENA, J., ed. (1998). Idempotency. Cambridge Univ. Press.
11. KINGMAN, J. F. C. (1968). The ergodic theory of subadditive stochastic processes. J. Roy. Statist. Soc. Ser. B 30 499-510.
12. MAIRESSE, J. (1997). Products of irreducible random matrices in the (max, +) algebra. Adv. in Appl. Probab. 29 444-477.
13. PERES, Y. (1991). Analytic dependence of Lyapunov exponents on transition probability. Proceedings of the Oberwolfach Conference. Lecture Notes in Math. 1486 64-80. Springer, Berlin.
14. PERES, Y. (1992). Domain of analytic continuation of the top Lyapunov exponent. Ann. Inst. H. Poincaré Probab. Statist. 28 131-148.
15. RUELLE, D. (1979). Analyticity properties of the characteristic exponents of random matrix products. Adv. Math. 32 68-80.
16. TSITSIKLIS, J. and BLONDEL, V. (1997). When is a pair of matrices mortal? Inform. Proc. Lett. 63 282-286.
17. VINCENT, J. M. (1997). Some ergodic results on stochastic iterative discrete event systems J. Discrete Event Dynamic Systems 7 209-232.