Lecture 3 Pseudo-random number generation

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Generation of N(µ,σ 2 ) distributed pseudo-random variables (1) Compute Z ∼ N(0, 1) (2) Z1 = µ + σZ Z1 is a pseudo-random number from a normal distribution N(µ,σ 2 ). Computational Finance – p. 32
How to generate a sample from a multidimensional normal distribution? Theorem. Let Z be a vector of p independent random variables each with a standard normal distribution N(0, 1). There exists a matrix A such that µ + AZ ∼ N(µ, Σ). Our aim is to find such a matrix A. We know how to generate a sequence of independent normally distributed random variables. Using matrix A we can transform it into a sequence of multidimensional normal variates. Computational Finance – p. 33
Page 1 and 2: Lecture 3 Pseudo-random number gene
Page 3 and 4: The numbers si have the following p
Page 5 and 6: Are the numbers Ui obtained with th
Page 7 and 8: Good congruential generator with a
Page 9 and 10: Apparently not so good congruential
Page 11 and 12: Fibonacci generators The original F
Page 13 and 14: ”Minimal Standard” generators W
Page 15 and 16: The Mersenne Twister The Mersenne T
Page 17 and 18: The state of the random number gene
Page 19 and 20: Generation of non-uniformly distrib
Page 21 and 22: Idea 2: Inversion of the distributi
Page 23 and 24: Idea 3: Transformation of random va
Page 25 and 26: If X ∼ N(µ, Σ), then X = (X1,X2
Page 27 and 28: We compute the determinant of the d
Page 29 and 30: Box-Muller with congruential genera
Page 31: Marsaglia algorithm The Box-Muller
Page 35 and 36: Algorithm for generation of N(µ,
Page 37 and 38: Simulation For Monte Carlo simulati
Page 39 and 40: PCA construction Principal Componen
Page 41 and 42: In general Cholesky decomposition a

Lecture 3 Pseudo-random number generation

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