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JOURNALS // Moscow Mathematical Journal

Mosc. Math. J., 2004, Volume 4, Number 2, Pages 441–453 (Mi mmj155)

Random walks and chemical networks
V. A. Malyshev, S. A. Pirogov, A. N. Rybko

References

1. A. Arkin, J. Ross, and H. McAdams, “Stochastic kinetic analysis of developmental pathway bifurcation in phage $\lambda$-infected Escherichia coli cells”, Genetics, 149 (1998), 1633–1648
2. S. N. Ethier and T. G. Kurtz, Markov processes. Characterization and convergence, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons Inc., New York, 1986  mathscinet  zmath
3. G. Gallavotti, “Ergodicity, ensembles, irreversibility in Boltzmann and beyond”, J. Statist. Phys., 78:5–6 (1995), 1571–1589  crossref  mathscinet  zmath  adsnasa
4. J. Hasty, F. Isaacs, M. Dolnik, D. McMillen, and J. J. Collins, Designer gene networks: Towards fundamental cellular control, Preprint
5. Russian Math. Surveys, 57:2 (2002), 241–304  mathnet  crossref  mathscinet  mathscinet  zmath
6. Probl. Inf. Transm., 36:2 (2000), 154–179  mathnet  mathscinet  mathscinet  zmath
7. M. A. Leontovich, “Main equations of kinetical theory of gases from the random processes point of view”, J. Experiment. Theoret. Phys., 5:3–4 (1935), 211–231 (Russian)  zmath
8. E. M. Lifshic and L. P. Pitaevskii, Theoretical physics, vol. 10, Nauka, Moscow, 1979 (Russian)  mathscinet
9. T. M. Liggett, Interacting particle systems, Die Grundlehren der Mathematischen Wissenschaften, 276, Springer-Verlag, Berlin etc., 1985  mathscinet  zmath
10. V. A. Malyshev, “Networks and dynamical systems”, Adv. in Appl. Probab., 25:1 (1993), 140–175  crossref  mathscinet  zmath
11. H. McAdams and A. Arkin, “Stochastic mechanisms in gene expression”, Proc. Natl. Acad. Sci. USA, 94 (1997), 814–819  crossref  adsnasa
12. D. A. McQuarrie, “Stochastic approach to chemical kinetics”, J. Appl. Probability, 4 (1967), 413–478  crossref  mathscinet  zmath
13. P. Whittle, Systems in stochastic equilibrium, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons Ltd., Chichester, 1986  mathscinet  zmath  adsnasa
14. K. Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften, 123, Springer-Verlag, Berlin etc., 1965  mathscinet


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