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1

Hugh, Gordon. Discrete probability. New York: Springer, 1997.

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2

Sachkov, Vladimir Nikolaevich. Probabilistic methods in discrete mathematics. Cambridge: Cambridge University Press, 1997.

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3

Alexander, Schied, ed. Stochastic finance: An introduction in discrete time. 2nd ed. New York: Walter de Gruyter, 2004.

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4

Alexander, Schied, ed. Stochastic finance: An introduction in discrete time. 3rd ed. Berlin: De Gruyter, 2011.

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5

Zelterman, Daniel. Discrete Distributions. New York: John Wiley & Sons, Ltd., 2005.

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6

Alexander, Schied, ed. Stochastic finance: An introduction in discrete time. Berlin: Walter de Gruyter, 2002.

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7

1964-, Merino Sandro, ed. Mathematical finance and probability: A discrete introduction. Basel, Switzerland: Birkhäuser, 2003.

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8

1964-, Merino Sandro, ed. Mathematical finance and probability: A discrete introduction. Boston, MA: Birkhauser Verlag, 2002.

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9

Probability and random processes: Using MATLAB with applications to continuous and discrete time systems. Chicago: Irwin, 1997.

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10

International Petrozavodsk Conference on Probabilistic Methods in Discrete Mathematics (5th 2000 Petrozavodsk, Russia). Probabilistic methods in discrete mathematics: Proceedings of the fifth international Petrozavodsk conference, Petrozavodsk, Russia, June 1-6, 2000. Edited by Kolchin V. F. Utrecht: VSP, 2002.

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11

Alon, Noga. The probabilistic method. 3rd ed. New York, NY: John Wiley, 2008.

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12

Alon, Noga. The probabilistic method. 3rd ed. New York, NY: John Wiley, 2008.

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13

Alon, Noga. The probabilistic method. 2nd ed. New York: Wiley, 2000.

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14

Alon, Noga. The probabilistic method. New York: Wiley, 1992.

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15

H, Spencer Joel, ed. The probabilistic method. Hoboken, New Jersey: John Wiley & Sons, Inc., 2016.

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16

Alon, Noga. The Probabilistic Method. New York: John Wiley & Sons, Ltd., 2005.

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17

Malyshev, V. A. Gibbs random fields: Cluster expansions. Dordrecht [Netherlands]: Kluwer Academic Publishers, 1991.

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18

Mathematics of probability. Providence, Rhode Island: American Mathematical Society, 2013.

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19

O, Seppäläinen Timo, ed. A course on large deviations with an introduction to Gibbs measures. Providence, Rhode Island: American Mathematical Society, 2015.

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20

Ontario. Esquisse de cours 12e année: Géométrie et mathématiques discrètes mga4u cours préuniversitaire. Vanier, Ont: CFORP, 2002.

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21

J, Aldous D., ed. Discrete probability and algorithms. New York: Springer-Verlag, 1995.

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22

1931-, Kesten Harry, ed. Probability on discrete structures. Berlin: Springer, 2004.

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23

F, Kolchin V., ed. Probabilistic problems of discrete mathematics: Collection of papers. Providence, R.I: American Mathematical Society, 1989.

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24

J, Aldous D., and Pemantle Robin, eds. Random discrete structures. New York: Springer, 1996.

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25

Random Discrete Structures. Springer, 2011.

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26

Editor), D. Aldous (Contributor, G. R. Grimmett (Contributor), C. D. Howard (Contributor), F. Martinelli (Contributor), J. M. Steele (Contributor), L. Saloff-Coste (Contributor), and Harry Kesten (Editor), eds. Probability on Discrete Structures. Springer, 2003.

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27

J, Aldous D., and Propp James 1960-, eds. Microsurveys in discrete probability: DIMACS workshop, June 2-6, 1997. Providence, RI: American Mathematical Society, 1998.

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28

Probabilities and Potential C - Potential Theory for Discrete and Continuous Semigroups. Elsevier, 1988. http://dx.doi.org/10.1016/s0304-0208(08)x7100-2.

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29

Kolchin, Valentin F. Probabilistic Methods in Discrete Mathematics: Proceedings of the Third International Petrozavodsk Conference (Progress in Pure and Applied Discrete Mathematics). Brill Academic Publishers, 1995.

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30

Dellacherie, Claude, P. A. Meyer, and C. Dellacherie. Probabilities & Potential: Potential Theory for Discrete & Continuous Semigroups (North-Holland Mathematics Studies). Elsevier Science Publishing Company, 1988.

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31

Discrete Structures With Contemporary Applications. CRC Press, 2011.

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32

Schied, Alexander. Stochastic Finance: An Introduction in Discrete Time. De Gruyter, Inc., 2011.

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33

Medina, Pablo Koch, and Sandro Merino. Mathematical Finance and Probability: A Discrete Introduction. Birkhauser, 2004.

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34

Basic discrete mathematics: Logic, set theory, & probability. World Scientific Publishing Co Pte Ltd, 2016.

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35

Probabilistic Methods in Discrete Mathematics: Proceedings of the Fourth International Petrozavodsk Conference, Petrozavodsk, Russia, June 3-7, 1996. Brill Academic Publishers, 1997.

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36

(Editor), Valentin F. Kolchin, V. Ya Kozlov (Editor), V. V. Mazalov (Editor), Yu L. Pavlov (Editor), and Yu V. Prokhorov (Editor), eds. Probabilistic Methods N Discrete Mathematics: Proceedings of the Fifth International Petrozavodsk Conference : Petrozavodsk, Russia, June 1-6, 2000. Brill Academic Publishers, 2002.

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37

Combinatorics of Compositions and Words (Discrete Mathematics and Its Applications). Chapman & Hall/CRC, 2009.

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38

Spencer, Joel H. The Probabilistic Method (Wiley-Interscience Series in Discrete Mathematics and Optimization). 3rd ed. Wiley-Interscience, 2008.

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39

Follmer, Hans, and Alexander Schied. Stochastic Finance: An Introduction in Discrete Time (De Gruyter Studies in Mathematics). Walter de Gruyter Inc, 2002.

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40

Zelterman, Daniel. Discrete Distributions: Applications in the Health Sciences. Wiley & Sons, Incorporated, John, 2008.

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41

Spencer, Joel H., and Noga Alon. Probabilistic Method. Wiley & Sons, Incorporated, John, 2008.

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42

Spencer, Joel H., and Noga Alon. Probabilistic Method. Wiley & Sons, Incorporated, John, 2015.

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43

Spencer, Joel H., and Noga Alon. Probabilistic Method. Wiley & Sons, Incorporated, John, 2015.

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44

Spencer, Joel H., and Noga Alon. Probabilistic Method. Wiley & Sons, Incorporated, John, 2011.

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45

Spencer, Joel H., and Noga Alon. Probabilistic Method. Wiley & Sons, Incorporated, John, 2008.

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46

Zelterman, Daniel. Discrete Distributions: Applications in the Health Sciences (Wiley Series in Probability and Statistics). Wiley, 2004.

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47

A, Nelder John, and Adams Niall M. 1968-, eds. Methods and models in statistics: In honour of Professor John Nelder, FRS. London: Imperial College Press, 2004.

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48

Stephens, Dave, Niall M. Adams, Martin Crowder, and D. J. Hand. Methods And Models In Statistics: In Honour Of Professor John Nelder, Frs. Imperial College Press, 2004.

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49

LO, Gane Samb, Aladji Babacar Niang, and Lois Chinwendu Okereke. A course of Elementary Probability Course. SPAS-EDS, 2020. http://dx.doi.org/10.16929/sts/2020.001.

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This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability theory. The theory is preceded by a general chapter on counting methods. Then, the theory of probabilities is presented in a discrete framework. Two objectives are sought. The first is to give the reader the ability to solve a large number of problems related to probability theory, including application problems in a variety of disciplines. The second is to prepare the reader before he takes course on the mathematical foundations of probability theory. In this later book, the reader will concentrate more on mathematical concepts, while in the present text, experimental frameworks are mostly found. If both objectives are met, the reader will have already acquired a definitive experience in problem-solving ability with the tools of probability theory and at the same time he is ready to move on to a theoretical course on probability theory based on the theory of Measure and Integration. The book ends with a chapter that allows the reader to begin an intermediate course in mathematical statistics.
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50

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Random graph ensembles. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0003.

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This chapter presents some theoretical tools for defining random graph ensembles systematically via soft or hard topological constraints including working through some properties of the Erdös-Rényi random graph ensemble, which is the simplest non-trivial random graph ensemble where links appear between two nodes with a fixed probability p. The chapter sets out the central representation of graph generation as the result of a discrete-time Markovian stochastic process. This unites the two flavours of graph generation approaches – because they can be viewed as simply moving forwards or backwards through this representation. It is possible to define a random graph by an algorithm, and then calculate the associated stationary probability. The alternative approach is to specify sampling weights and then to construct an algorithm that will have these weights as the stationary probabilities upon convergence.
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