Free Access
Issue
ESAIM: M2AN
Volume 48, Number 6, November-December 2014
Page(s) 1757 - 1775
DOI https://doi.org/10.1051/m2an/2014018
Published online 03 October 2014
  1. P. Deuflhard, W. Huisinga, T. Jahnke and M. Wulkow, Adaptive discrete Galerkin methods applied to the chemical master equation. SIAM J. Sci. Comput. 30 (2008) 2990–3011. [CrossRef] [Google Scholar]
  2. S.V. Dolgov and B.N. Khoromskij, Simultaneous state-time approximation of the chemical master equation using tensor product formats. arXiv:1311.3143 (2013). [Google Scholar]
  3. S. Engblom, Spectral approximation of solutions to the chemical master equation. J. Comput. Appl. Math. 229 (2009) 208–221. [CrossRef] [Google Scholar]
  4. D.T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22 (1976) 403–434. [Google Scholar]
  5. D.T. Gillespie, A rigorous derivation of the chemical master equation. Phys. A 188 (1992) 404–425. [Google Scholar]
  6. D.T. Gillespie, Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58 (2007) 35–55. [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  7. M. Hegland, Approximating the solution of the chemical master equation by aggregation. ANZIAM J. 50 (2008) C371–C384. [Google Scholar]
  8. M. Hegland and J. Garcke, On the numerical solution of the chemical master equation with sums of rank one tensors. ANZIAM J. Electron. Suppl. 52 (2010) C628–C643. [Google Scholar]
  9. M. Hegland, A. Hellander and P. Lötstedt, Sparse grids and hybrid methods for the chemical master equation. BIT 48 (2008) 265–283. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Hellander and P. Lötstedt, Hybrid method for the chemical master equation. J. Comput. Phys. 227 (2007) 100–122. [CrossRef] [Google Scholar]
  11. D.J. Higham, Modeling and simulating chemical reactions. SIAM Rev., 50:347–368, 2008. [Google Scholar]
  12. S. Ilie, W.H. Enright and K.R. Jackson, Numerical solution of stochastic models of biochemical kinetics. Can. Appl. Math. Q. 17 (2009) 523–554. [MathSciNet] [Google Scholar]
  13. T. Jahnke, On reduced models for the chemical master equation. Multiscale Model. Simul. 9 (2011) 1646–1676. [CrossRef] [Google Scholar]
  14. T. Jahnke and W. Huisinga, A dynamical low-rank approach to the chemical master equation. Bull. Math. Biol. 70 (2008) 2283–2302. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  15. T. Jahnke and T. Udrescu, Solving chemical master equations by adaptive wavelet compression. J. Comput. Phys. 229 (2010) 5724–5741. [CrossRef] [Google Scholar]
  16. V. Kazeev, M. Khammash, M. Nip and Ch. Schwab, Direct solution of the chemical master equation using quantized tensor trains. PLoS Comput. Biol. 10 (2014) e1003359. [CrossRef] [PubMed] [Google Scholar]
  17. W. Ledermann and G.E.H. Reuter, Spectral theory for the differential equations of simple birth and death processes. Phil. Trans. R. Soc. A 246 (1954) 321–369. [CrossRef] [Google Scholar]
  18. M. Martcheva, H.R. Thieme and T. Dhirasakdanon, Kolmogorov’s differential equations and positive semigroups on first moment sequence spaces. J. Math. Biol. 53 (2006) 642–671. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  19. S. Menz, J.C. Latorre, C. Schütte and W. Huisinga, Hybrid stochastic-deterministic solution of the chemical master equation. Multiscale Model. Simul. 10 (2012) 1232–1262. [CrossRef] [Google Scholar]
  20. B. Munsky and M. Khammash, The finite state projection algorithm for the solution of the chemical master equation. J. Chem. Phys. 124 (2006) 044104. [CrossRef] [PubMed] [Google Scholar]
  21. G.E.H. Reuter and W. Ledermann, On the differential equations for the transition probabilities of Markov processes with enumerably many states. Proc. Cambridge Philos. Soc. 49 (1953) 247–262. [CrossRef] [MathSciNet] [Google Scholar]
  22. V. Sunkara and M. Hegland, An optimal finite state projection method. Procedia Comput. Sci. 1 (2012) 1579–1586. [CrossRef] [Google Scholar]
  23. H.R. Thieme and J. Voigt, Stochastic semigroups: their construction by perturbation and approximation, in Positivity IV-theory and applications. Tech. Univ. Dresden, Dresden (2006) 135–146. [Google Scholar]
  24. T. Udrescu, Numerical methods for the chemical master equation. Doctoral Thesis, Karlsruher Institut für Technologie (2012). [Google Scholar]

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