References

  1. William J. Anderson (1991): Continuous-Time Markov Chains: An Applications-Oriented Approach. Springer Verlag, doi:10.1007/978-1-4612-3038-0.
  2. Adnan Aziz, Kumud Sanwal, Vigyan Singhal & Robert K. Brayton (2000): Model-Checking Continuous-Time Markov Chains. ACM Trans. Comput. Log 1(1), pp. 162–170, doi:10.1145/343369.343402.
  3. Christel Baier, Boudewijn R. Haverkort, Holger Hermanns & Joost-Pieter Katoen (2003): Model-Checking Algorithms for Continuous-Time Markov Chains. IEEE Trans. Software Eng 29(6), pp. 524–541, doi:10.1109/TSE.2003.1205180.
  4. P. Ballarini, R. Mardare & I. Mura (2009): Analysing Biochemical Oscillation through Probabilistic Model Checking. In: Proc. 2nd Workshop From Biology to Concurrency and Back (FBTC'08), Electronic Notes in Theoretical Computer Science 229 (issue 1). Elsevier, pp. 3–19, doi:10.1016/j.entcs.2009.02.002.
  5. P.-J. Courtois & P Semal (1984): Bounds for the Positive Eigenvectors of Nonnegative Matrices and for their Approximations by Decomposition. J. ACM 31(4), pp. 804–825, doi:10.1145/1634.1637.
  6. Pierre-Jacques Courtois (1985): Analysis of Large Markovian Models by Parts. Applications to Queueing Network Models. In: Messung, Modellierung und Bewertung von Rechensystemen, 3. GI/NTG-Fachtagung, pp. 1–10, doi:10.1007/978-3-642-87472-7_1.
  7. Tuğrul Dayar, Holger Hermanns, David Spieler & Verena Wolf (2011): Bounding the equilibrium distribution of Markov population models. Numerical Linear Algebra with Applications 18(6), pp. 931–946, doi:10.1002/nla.795.
  8. Nico M. van Dijk (1988): On the finite horizon Bellman equation for controlled Markov jump models with unbounded characteristics. Stochastic Proc. Appl 28, pp. 141–157, doi:10.1016/0304-4149(88)90071-3.
  9. E. Allen Emerson & Edmund M. Clarke (1982): Using Branching Time Temporal Logic to Synthesize Synchronization Skeletons. Sci. Comput. Program 2(3), pp. 241–266, doi:10.1016/0167-6423(83)90017-5.
  10. P. Glynn & A. Zeevi (2008): Bounding stationary expectations of Markov processes. IMS Collections: Markov Processes and Related Topics 4, pp. 195–214, doi:10.1214/074921708000000381.
  11. Winfried K. Grassmann (1991): Finding Transient Solutions in Markovian Event Systems Through Randomization. In: Numerical Solution of Markov Chains, pp. 357–371.
  12. Peter J. E. Gross & Jean Peccoud (1998): Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. Proc. Natl. Acad. Sci. 95, pp. 6750–6755, doi:10.1073/pnas.95.12.6750.
  13. Takayuki Gunji, Sunyoung Kim, Masakazu Kojima, Akiko Takeda, Katsuki Fujisawa & Tomohiko Mizutani (2004): PHoM – a Polyhedral Homotopy Continuation Method for Polynomial Systems. Computing 73(1), pp. 57–77, doi:10.1007/s00607-003-0032-4.
  14. E. Moritz Hahn, Holger Hermanns, Björn Wachter & Lijun Zhang (2009): INFAMY: An Infinite-State Markov Model Checker. In: CAV. Springer, pp. 641–647, doi:10.1007/978-3-642-02658-4_49.
  15. E. Moritz Hahn, Holger Hermanns, Björn Wachter & Lijun Zhang (2009): Time-Bounded Model Checking of Infinite-State Continuous-Time Markov Chains. Fundamenta Informaticae 95, pp. 129–155, doi:10.3233/FI-2009-145.
  16. Joost-Pieter Katoen, Daniel Klink, Martin Leucker & Verena Wolf (2007): Three-Valued Abstraction for Continuous-Time Markov Chains. In: CAV, Lecture Notes in Computer Science 4590. Springer, pp. 311–324, doi:10.1007/978-3-540-73368-3_37.
  17. Daniel Klink (2010): Three-Valued Abstraction for Stochastic Systems. RWTH Aachen.
  18. T. L. Lee, T. Y. Li & C. H. Tsai (2008): HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method. Computing 83(2-3), pp. 109–133, doi:10.1007/s00607-008-0015-6.
  19. A. Loinger, A. Lipshtat, N. Q. Balaban & O. Biham (2007): Stochastic simulations of genetic switch systems. Physical Review E 75(2), pp. 021904, doi:10.1103/PhysRevE.75.021904.
  20. Aad P. A. van Moorsel & William H. Sanders (1994): Adaptive Uniformization. Communications in Statistics - Stochastic Models 10(3), pp. 619–647, doi:10.1080/15326349408807313.
  21. Brian Munsky & Mustafa Khammash (2006): The Finite State Projection Algorithm for the Solution of the Chemical Master Equation. Journal of Chemical Physics 124(044104), doi:10.1063/1.2145882.
  22. Anne Remke, Boudewijn R. Haverkort & Lucia Cloth (2007): CSL Model Checking Algorithms for QBDs. Theor. Comput. Sci 382(1), pp. 24–41. Available at http://dx.doi.org/10.1016/j.tcs.2007.05.007.
  23. D. Spieler (2011): Geobound. http://mosi.cs.uni-saarland.de/?page_id=74.
  24. William J. Stewart (1994): Introduction to the Numerical Solution of Markov Chains. Princeton University Press.
  25. M. Thattai & A. van Oudenaarden (2001): Intrinsic noise in gene regulatory networks.. Proceedings of the National Academy of Science, USA 98(15), pp. 8614–8619, doi:10.1073/pnas.151588598.
  26. R. Tweedie (1975): Sufficient conditions for regularity, recurrence and ergodicity of Markov processes. Math. Proc. Camb. Phil. Soc. 78, pp. 125–130, doi:10.1017/S0305004100051562.

Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org