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1

Rubino, Gerardo, and Bruno Tuffin, eds. Rare Event Simulation using Monte Carlo Methods. Chichester, UK: John Wiley & Sons, Ltd, 2009. http://dx.doi.org/10.1002/9780470745403.

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2

Niederreiter, Harald. Random numbergeneration and quasi-Monte Carlo methods. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1992.

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3

István, Deák. Random number generators and simulation. Budapest: Akadémiai Kiadó, 1990.

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4

Random number generation and Monte Carlo methods. New York: Springer, 1998.

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5

Random number generation and Monte Carlo methods. 2nd ed. New York: Springer-Verlag, 2003.

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6

Random number generation and quasi-Monte Carlo methods. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1992.

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7

István, Deák. Véletlenszám-generátorok és alkalmazásuk. Budapest: Akadémiai Kiadó, 1986.

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8

Uniform random numbers: Theory and practice. Boston, Mass: Kluwer Academic Publishers, 1995.

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9

Rubino, Gerardo, and Bruno Tuffin. Rare Event Simulation Using Monte Carlo Methods. Wiley & Sons, Incorporated, John, 2009.

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10

1955-, Rubino Gerardo, and Tuffin Bruno, eds. Rare event simulation using Monte Carlo methods. Hoboken, N.J: Wiley, 2009.

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11

Boudreau, Joseph F., and Eric S. Swanson. Monte Carlo methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0007.

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Monte Carlo methods are those designed to obtain numerical answers with the use of random numbers . This chapter discusses random engines, which provide a pseudo-random pattern of bits, and their use in for sampling a variety of nonuniform distributions, for both continuous and discrete variables. A wide selection of uniform and nonuniform variate generators from the C++ standard library are reviewed, and common techniques for generating custom nonuniform variates are discussed. The chapter presents the uses of Monte Carlo to evaluate integrals, particularly multidimensional integrals, and then introduces the important method of Markov chain Monte Carlo, suitable for solving a wide range of scientific problems that require the sampling of complicated multivariate distributions. Relevant topics in probability and statistics are also introduced in this chapter. Finally, the topics of thermalization, autocorrelation, multimodality, and Gibbs sampling are presented.
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12

Gentle, James E. Random Number Generation and Monte Carlo Methods (Statistics and Computing). Springer, 2004.

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13

Peter, Hellekalek, and Larcher Gerhard, eds. Random and quasi-random point sets. New York: Springer, 1998.

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14

Niederreiter, Harald. Random Number Generation and Quasi-Monte Carlo Methods (CBMS-NSF Regional Conference Series in Applied Mathematics). Society for Industrial Mathematics, 1987.

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15

Tezuka, Shu. Uniform Random Numbers. Springer, 2012.

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16

Uniform Random Numbers. Springer My Copy UK, 1995.

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