11.R: Footnotes and References

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Aug 4, 2023
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- 11.5: Mean First Passage Time for Ergodic Chains
- 12: Random Walks

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Footnotes

R. A. Howard, Dynamic Probabilistic Systems, vol. 1 (New York: John Wiley and Sons, 1971).
J. G. Kemeny, J. L. Snell, G. L. Thompson, Introduction to Finite Mathematics, 3rd ed. (Englewood Cliffs, NJ: Prentice-Hall, 1974).
P. and T. Ehrenfest, "Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem," Physikalishce Zeitschrift, vol. 8 (1907), pp. 311-314.
S. Sawyer, "Results for The Stepping Stone Model for Migration in Population Genetics," Annals of Probability, vol. 4 (1979), pp. 699-728.
H. Gonshor, "An Application of Random Walk to a Problem in Population Genetics," Amercan Math Monthly, vol. 94 (1987), pp. 668-671
Private communication.
Roberts, Discrete Mathematical Models (Englewood Cliffs, NJ: Prentice Hall, 1976).
W. W. Leontief, Input-Output Economics (Oxford: Oxford University Press, 1966).
L. J. Guibas and A. M. Odlyzko, "String Overlaps, Pattern Matching, and Non-transitive Games," Journal of Combinatorial Theory, Series A, vol. 30 (1981), pp. 183-208.
Penney, "Problem: Penney-Ante," Journal of Recreational Math, vol. 2 (1969), p. 241.
M. Gardner, "Mathematical Games," Scientific American, vol. 10 (1974), pp. 120-125.Guibas and Odlyzko, op. cit.
E. Seneta, Non-Negative Matrices: An Introduction to Theory and Applications, Wiley, New York, 1973, pp. 52-54.
Engle, Wahrscheinlichkeitsrechnung und Statistik, vol. } 2 \text { (Stuttgart: Klett Verlag, 1976).
E. G. Coffman, J. T. Kaduta, and L. A. Shepp, "On the Asymptotic Optimality of First Storage Allocation," IEEE Trans. Software Engineering, vol. II (1985), pp. 235-239.
Doeblin, "Expose de la Theorie des Chaines Simple Constantes de Markov a un Nombre Fini d'Etats," Rev. Mach. de l'Union Interbalkanique, vol. 2 (1937), pp. 77-105.
Lindvall, Lectures on the Coupling Method (New York: Wiley 1992).
See Dictionary of Scientific Biography, ed. C. C. Gillespie (New York: Scribner's Sons, 1970), pp. 124-130.
A. A. Markov, "An Example of Statistical Analysis of the Text of Eugene Onegin Illustrating the Association of Trials into a Chain," Bulletin de l'Acadamie Imperiale des Sciences de St. Petersburg, ser. 6, vol. 7 (1913), pp. 153-162.
C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (Urbana: Univ. of Illinois Press, 1964).
M. Frechet, "Théorie des événements en chaine dans le cas d'un nombre fini d'états possible," in Recherches théoriques Modernes sur le calcul des probabilités, vol. 2 (Paris, 1938).
J. G. Kemeny and J. L. Snell, Finite Markov Chains.
Private communication.
Private communication.

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