Bounding the lumping error in Markov chain dynamics

Applied Mathematics Letters

Volumn 22, Issue 9, 2009, Pages 1471-1475

  Hoffmann, Karl Heinz ^a   Salamon, Peter ^b  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

^b SAN DIEGO STATE UNIVERSITY   (United States)

Author keywords

Coarse graining error; Lumped dynamics; Lumped states; Markov chain; State space dynamics

Indexed keywords

COARSE GRAINING ERROR; LUMPED DYNAMICS; LUMPED STATES; MARKOV CHAIN; STATE SPACE DYNAMICS;

DYNAMICS;

MARKOV PROCESSES;

EID: 67349151777     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2009.03.016     Document Type: Article

References (15)

1. Yin G.G., and Zhang Q. Discrete-Time Markov Chains: Two-Time-Scale Methods and Applications. Applications of Mathematics vol. 55 (2005), Springer, New York
2. Hillier F.S., and Lieberman G.J. Introduction to Operations Research. 8th edition (2005), McGraw-Hill Higher Education, Boston
3. Peyton Young H. Social Dynamics: Theory and Applications. In: Tesfatsion L., and Judd K.L. (Eds). Handbook of Computational Economics vol. II (2006), North Holland, Amsterdam 1081-1108 (Chapter 22)
4. Hammond B.L., Lester Jr. W.A., and Reynolds P.J. Monte Carlo Methods in Ab Initio Quantum Chemistry. World Scientific Lecture and Course Notes in Chemistry (1994), World Scientific, Singapore
5. van Kampen N.G. Stochastic Processes in Physics and Chemistry. 2nd edition (1992), North-Holland, Amsterdam
6. Oppenheim I., Shuler K.E., and Weiss G.H. Stochastic Processes in Chemical Physics: The Master Equation (1977), MIT Press, Cambridge, MA
7. Caswell H. Matrix Population Models: Construction, Analysis, and Interpretation. 2nd edition (2001), Sinauer, Sunderland, MA
8. Shridharbhai Trivedi K. Probability and Statistics with Reliability, Queueing, and Computer Science Applications (1982), Prentice-Hall, Englewood Cliffs, NJ
9. In: Gilks W.R., Richardson S., and Spiegelhalter D. (Eds). Markov Chain Monte Carlo in Practice (1996), Chapman & Hall, London
10. In: Kemeny J.G., and Snell J.L. (Eds). Finite Markov chains (1960), Van Nostrand, Princeton, NJ
11. Andresen B., Hoffmann K.H., Mosegaard K., Nulton J., Pedersen J.M., and Salamon P. On lumped models for thermodynamic properties of simulated annealing problems. J. Phys. France 49 (1988) 1485-1492
12. Avrachenkov K.E., and Haviv M. The first Laurent series coefficients for singularly perturbed stochastic matrices. Linear Algebra Appl. 386 (2004) 243-259
13. Jerrum M., Son J.-B., Tetali P., and Vigoda E. Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains. Ann. Appl. Probab. 14 4 (2004) 1741-1765
14. Burke C.J., and Rosenblatt M. A Markovian function of a Markov chain. Annals of Mathematical Statistics 29 4 (1958) 1112-1122
15. Rothblum U.G., and Tan C.P. Upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices. Linear Algebra Appl. 66 (1985) 45-86