Générateurs de nombres aléatoires - Jean

a c n
u0≤n, ∀k≥0, uk+1 =auk+cmod n.
uk
n[0,1]
uk+1 = 65539ukmod 231 u0
uk+1 = 129uk+ 907633385 mod 232
uk+1 = 69069ukmod 232
rand()
1012
n
u
u au +cmod n u
xk
1
NPN
k=1 xk1
2N+∞
[0,1]
x x
[a, b] [0,1] b−a N
KN[a, b]KN
N
b−a N +∞

x
x[0,1]
F(x) = x
[0,1]
[0,1] Fl(x) = k
NN k
x
l N
εN= sup |Fl(x)−F(x)|F(x) = x
εN
N
dNε>dN5%
d20 = 0.294, d50 = 0.188, d100 = 0.150 N > 100 dN=1.358
√N.
(xk)
(xk, xk+1) [0,1]2
(6xk+1 −9xk, xk+2)

n= 28= 256 a
c