Skip to main content

Modeling Electrochemical Phenomena via Markov Chains and Processes

  • Chapter
Modern Aspects of Electrochemistry

Part of the book series: Modern Aspects of Electrochemistry ((MAOE,volume 39))

  • 1129 Accesses

Abstract

Named after the Russian mathematician Andrei Andreievich Markov (1856-1922), Markov chains and processes express the probability evolution of events, whose future, loosely speaking, is independent of their past. The terminological difference between the two designations is that Markov chains are related to discrete events, whereas Markov processes are related to continuous events.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. A. Tamir, Application of Markov Chains in Chemical Engineering, Elsevier, Amsterdam, 1998.

    Google Scholar 

  2. V. S. Pugachev, Teoriya Sluchainikh Funktzii (Theory of Random Functions), Gos. Izd. Fiziko-Matem. Liter., 2nd Ed., Moscow, 1960, Section 46, pp. 191–202.

    Google Scholar 

  3. E. Parzen, Modern Probability Theory and Its Applications, Wiley and Sons, New York, 1960, Chapter 3, Section 3, pp. 136–147.

    Google Scholar 

  4. H. Stark and J. W. Woods, Probability, Random Processes and Estimation Theory for Engineers, Prentice Hall, Englewood Cliffs, 1986.

    Google Scholar 

  5. Y. A. Rozanov, Probability Theory: A Concise Course, Dover, New York, 1969, Chapter 7, pp. 83–101; Chapter 8, pp. 102–114.

    Google Scholar 

  6. A. A. Sveshnikov, Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions, Dover, 1968, Chapter VIII, pp. 231–274.

    Google Scholar 

  7. F. R. Gantmacher, The Theory of Matrices, Chelsea Publishing, New York, 1959, Vol. 2, Chapter XIII, Sections 6–8, pp. 80–98.

    Google Scholar 

  8. M. D. Greenberg, Advanced Engineering Mathematics, 2nd Ed., Prentice Hall, Upper Saddle River, 1998, Section 11.2, pp. 546–549.

    Google Scholar 

  9. W. J. Stewart, Introduction to the Numerical Solution of Markov Chains, Princeton Univ. Press, 1994.

    Google Scholar 

  10. A. Sinclair, Algorithms for Random Generation and Counting: a Markov Chain Approach, Birehäuser, Boston, 1993.

    Google Scholar 

  11. W. J. Anderson, Continuous-Time Markov Chains: An Applications-Oriented Approach, Springer-Verlag, New York, 1991.

    Google Scholar 

  12. O. Hernandez-Lerma, Adaptive Markov Control Processes, Springer-Verlag, New York, 1989.

    Google Scholar 

  13. G. Winkler, Image Analysis, Random Fields and Markov Chain Monte Carlo Methods, Springer-Verlag, New York, 2003.

    Google Scholar 

  14. P. Baldi, L. Mazliak, and P. Priouret, Martingales and Markov Chains, Chapman and Hall/CRC, Boca Raton, 2002.

    Google Scholar 

  15. T. Z. Fahidy, Can. J. Chem. Eng. 65 (1987) 1009.

    Article  CAS  Google Scholar 

  16. G. Radons, J. D. Becker, B. Duelfer, and J. Krueger, Biol. Cybern. 71 (1994) 359.

    Article  CAS  Google Scholar 

  17. A. Oprişan, S.-A. Oprişan, and M. Ignat, Analele Stiintifice Ale Universitătii “Al.I. Guza”, (in English), Iasi (Romania), 1997–1998.

    Google Scholar 

  18. S. A. Godorr, B. D. Young and A. W. Bryson, Chem. Eng. Commun. 117 (1992) 307.

    Article  CAS  Google Scholar 

  19. T. Witten and L. M. Sauder, Phys. Rev. Lett. 47 (1981) 1400.

    Article  CAS  Google Scholar 

  20. T. Witten, and L. M. Sauder, Phys. Rev. B 27 (1983) 5686.

    Article  Google Scholar 

  21. F. Argoul, A. Arneodo, G. Grasseau, and H. L. Swinney, Phys. Rev. Lett. 61 (1988) 2558.

    Article  CAS  Google Scholar 

  22. M. R. Dudek, W. M. Trochimczuk, and R. Wycizk, J. Membrane Sci. 67 (1992) 273.

    Article  CAS  Google Scholar 

  23. T. Z. Fahidy, J. Appl. Electrochem. 17 (1987) 841.

    Article  CAS  Google Scholar 

  24. L. J. Goldstein, and D. I. Schneider, Finite Mathematics and Its Applications, 2nd Ed., Prentice Hall, Englewood Cliffs, 1984, Chapter 8, pp. 329–360.

    Google Scholar 

  25. T. Z. Fahidy, Chem. Eng. Edu. 27 (1993) 42.

    CAS  Google Scholar 

  26. D. C. Montgomery, G. C. Runger, and N. F. Hubele, Engineering Statistics, 2nd Ed., Wiley and Sons, New York, 2001, Section 2.1, Exercise 2.3, p. 25.

    Google Scholar 

  27. Z. H. Gu, J. Chen, and T. Z. Fahidy, Electrochim. Acta 37 (1992) 2637.

    Article  CAS  Google Scholar 

  28. T. Z. Fahidy, J. Appl. Electrochem. 28 (1998) 411.

    Article  CAS  Google Scholar 

  29. J. O'M. Bockris, A. K. N. Reddy, and M. Gamboa-Aldeco, Modern Electrochemistry, 2nd Ed., Plenum, New York, Volume 2A: Fundamentals of Electrodics, Section 6.2.6.2, p. 804.

    Google Scholar 

  30. L. H. Van Vleck, Elements of Materials Science and Engineering, 4th Ed., Addison-Wesley, Reading, Mass., 1980, Appendix B, pp. 520–523.

    Google Scholar 

  31. K. Scott, Electrochemical Reaction Engineering, Acad. Press, London, 1991, Section 2.1.2, pp. 52–56.

    Google Scholar 

  32. T. Z. Fahidy, unpublished results

    Google Scholar 

  33. C. Dixon, Linear Algebra, Van Nostrand Reinhold, New York, 1971, Section VII. 1, pp. 135–140.

    Google Scholar 

  34. H. S. Wilf, Mathematics for the Physical Sciences, Dover, New York, 1962, Section 1,12, pp. 18–20.

    Google Scholar 

  35. W. K. Nicholson, Elementary Linear Algebra With Applications, Prindle, Weber and Smith, Boston, 1986, Section 7.1, pp. 311–324

    Google Scholar 

  36. A. J. Bard, and L. R. Faulkner, Electrochemical Methods, Wiley and Sons, New York, 1980, Section 7.7.2, pp. 273–274.

    Google Scholar 

  37. Idem, ibid. Section 7.7.3, pp. 275–276.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this chapter

Cite this chapter

Fahidy, T.Z. (2006). Modeling Electrochemical Phenomena via Markov Chains and Processes. In: Vayenas, C., White, R.E., Gamboa-Adelco, M.E. (eds) Modern Aspects of Electrochemistry. Modern Aspects of Electrochemistry, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31701-4_3

Download citation

Publish with us

Policies and ethics