Comparison Methods For Stochastic Models And Risks Rating: 9,9/10 5940 votes
  1. Stochastic Process
  1. Abu-Amsha, O., Vincent, J.M.: An algorithm to bound functionals of Markov chains with large state space. In: 4th INFORMS Conference on Telecommunications, Boca Raton, Florida (1998)Google Scholar
  2. Benmammoun, M., Busic, A., Fourneau, J.M., Pekergin, N.: Increasing convex monotone Markov chains: theory, algorithms and applications. In: Markov Anniversary Meeting, pp. 189–210. Boson Books (2006)Google Scholar
  3. Busic, A., Fourneau, J.M.: Bounds for Point and Steady-State Availability: An Algorithmic Approach Based on Lumpability and Stochastic Ordering. In: Bravetti, M., Kloul, L., Zavattaro, G. (eds.) EPEW, WS-FM 2005. LNCS, vol. 3670, pp. 94–108. Springer, Heidelberg (2005)Google Scholar
  4. Courtois, P., Semal, P.: Bounds for the positive eigenvectors of nonnegative matrices and for their approximations by decomposition. J. of ACM 31, 804–825 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  5. Dayar, T., Fourneau, J.M., Pekergin, N.: Transforming stochastic matrices for stochastic comparison with the st-order. RAIRO-RO 37, 85–97 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  6. Dayar, T., Pekergin, N., Younes, S.: Conditional Steady-State Bounds for a Subset of States in Markov Chains. In: SMCTools, Pisa, Italy (2006)Google Scholar
  7. Fourneau, J.M., Le Coz, M., Quessette, F.: Algorithms for an irreducible and lumpable strong stochastic bound. Linear Algebra and Applications 386, 167–186 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  8. Fourneau, J.M., Le Coz, M., Pekergin, N., Quessette, F.: An open tool to compute stochastic bounds on steady-state distributions and rewards. In: IEEE Mascots 2003, Orlando, USA (2003)Google Scholar
  9. Fourneau, J.M., Pekergin, N.: An algorithmic approach to stochastic bounds. In: Calzarossa, M.C., Tucci, S. (eds.) Performance 2002. LNCS, vol. 2459, pp. 64–88. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. Haddad, S., Moreaux, P.: Sub-stochastic matrix analysis for bounds computation-Theoretical results. Eur. Jour. of Operational. Res. 176, 999–1015 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  11. Meyer, C.D.: Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems. SIAM Review 31(2), 240–272 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  12. Meyer, C.D.: Matrix Analysis and Applied Linear Algebra. SIAM (2000)Google Scholar
  13. Pekergin, N., Dayar, T., Alparslan, D.: Compenent-wise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering. Eur. Jour. of Op. Res. 165, 810–825 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  14. Muller, A., Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, New York (2002)Google Scholar
  15. Shaked, M., Shantikumar, J.G.: Stochastic Orders and Their Applications. Academic Press, San Diago (1994)zbMATHGoogle Scholar
  16. Trivedi, K.S.: Probability and Statistic with Reliability, Queueing and Computer Science Applications. Second Edition, Wiley (2002)Google Scholar
  17. Truffet, L.: Near Complete Decomposability: Bounding the error by a Stochastic Comparison Method. App. Prob. 29, 830–855 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  18. Truffet, L.: Reduction Technique For Discrete Time Markov Chains on Totally Ordered State Space Using Stochastic Comparisons. Journal of Applied Probability 37(3) (2000)Google Scholar
  19. Zhao, Y.Q., Liu, D.: The Censored Markov chain and the Best Augmentation. Jour. of App. Prob. 33, 623–629 (1996)zbMATHCrossRefMathSciNetGoogle Scholar

Stochastic Process

Handbook of stochastic methods

Sucrose accumulation model in sugar cane culm tissue BIOMD from Biomodels database 11,15, further referred to as model A, and yeast glycolysis model BIOMD, further referred to as model B, are used to test the performance of several global stochastic optimisation methods.The COPASI software is used as optimisation tool due to well-developed graphical user interface.