PC 7 TCL, Méthode de Monte-Carlo

X1, X2, . . . ΦX(t) = E[eitX ]N≥1
gN(z) = E[zN]N
XkE[X1]<∞E[N]<∞
S=X1+··· +XN,
SE[S]E[X1],E[N]
N(0,1)
12 [0,1] 6
20000 U1+··· +U12 −6N(0,1)
p
n Fn
Fn
In95 p
limnP(In3p)≥0.95
Z∼ N(0,1) P(−1.96 ≤Z≤1.96) = 0.95
P|Binom(n, p)−np|> r≤2 exp −2r2
n.
Jn95 p
nP(Jn3p)≥0.95

(Xn)n≥1E[X1]=0 E[X2
1]<+∞
lim
n→+∞
P(X1+··· +Xn≥0) = 1/2.
g
0≤g≤1m=
R1
0g(x)dx
X Y [0,1]
U=1Y≤g(X), V =g(X)W=g(X) + g(1 −X)
2.
U, V W
m
gE(g(X)g(1 −X)) ≤m2
(g(x)−g(y))(g(1 −x)−g(1 −y)) ≤0
x, y
(Xi)i≥1[0,1]
An=1
2n
2n
X
i=1
g(Xi), Bn=1
2n
n
X
i=1
(g(Xi) + g(1 −Xi)),
m
(Xi)i≥10
Pn
i=1 Xi
pPn
i=1 X2
i
?
?
(Xn)nσ2>0
Zn=1
σ√n
n
X
j=1
Xj.
(Zn)
Z2n−Zn
(Z2n−Zn)n≥1
(Zn)X