Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 2, 2011, Pages

  Martirosyan, A ^a   Saakian, David B ^b,c,d  

^a YEREVAN STATE UNIVERSITY   (Armenia)

^b INSTITUTE OF PHYSICS   (Taiwan)

^c YEREVAN PHYSICS INSTITUTE   (Armenia)

^d NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; CHEMICAL MASTER EQUATION; EXACT RESULTS; EXPLICIT EXPRESSIONS; HAMILTON JACOBI EQUATIONS; LARGE SYSTEM SIZE; ONE-DIMENSIONAL CHAINS; STATIONARY NOISE; SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS; TIME-DEPENDENT;

PROBABILITY DISTRIBUTIONS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 80051635935     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.021122     Document Type: Article

References (21)

1. R. Phillips, J. Kondev, and J. Theriot, Physical Biology of the Cell (Garland Science, New York, 2008).
2. D. A. Beard and H. Qian, in Chemical Biophysics: Quantitative Analysis of Cellular Systems, Cambridge Texts in Biomedical Engineering (Cambridge University Press, New York, 2008).
3. C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985).
4. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier Science, North-Holland, 2007).
5. T. Lux, J. Econ. Behav. Organ. 0167-2681 10.1016/j.jebo.2009.07.003 72, 638 (2009).
6. H. Ge and H. Qian, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 103.148103 103, 148103 (2009).
7. J. E. Ferrell and W. Xiong, Chaos CHAOEH 1054-1500 10.1063/1.1349894 11, 227 (2001).
8. G. Hu, Physica A PHYADX 0378-4371 10.1016/0378-4371(86)90271-2 136, 607 (1986).
9. H. Woodcock and P. G. Higgs, J. Theor. Biol. JTBIAP 0022-5193 10.1006/jtbi.1996.0049 179, 61 (1996). (Pubitemid 26137782)
10. E. Baake and H. Wagner, Genet. Res. GENRA8 0016-6723 10.1017/ S0016672301005110 78, 93 (2001). (Pubitemid 32755324)
11. D. B. Saakian, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-007-9334-9 128, 781 (2007).
12. K. Sato and K. Kaneko, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75. 061909 75, 061909 (2007). (Pubitemid 47140269)
13. D. B. Saakian, O. Rozanova, and A. Akmetzhanov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.041908 78, 041908 (2008).
14. J. Keizer, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.75.7.3023 75, 3023 (1978).
15. R. and S. J. Chapman, Eur. J. Appl. Math. JSTPBS 0956-7925 10.1017/S0956792505006194 16, 427 (2005). (Pubitemid 43235030)
16. M. Assaf and B. Meerson, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.021116 81, 021116 (2010).
17. C. Escudero and A. Kamenev, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.041149 79, 041149 (2009).
18. L. C. Evans, Partial Differential Equations (Providence, RI, 1999).
19. A. Melikyan, Generalized Characteristics of First Order PDEs (Birkhäuser, Boston, 1998).
20. M. Vellela and H. Qian, J. R. Soc. Interface 6, 925 (2009).
21. X. S. Xie, in Single Molecule Spectroscopy in Chemistry, Physics and Biology Nobel Symposium, edited by, Astrid Graslund, Springer Series in Chemical Physics (Springer-Verlag, Berlin, 2010), pp. 435-448.