à cette adresse

f:P−→ P
~
θ7−→ ~ θ·R
Q
F
(µ, ν)∈S2
θ=µ−ν
X
i
θ(i) = X
i
µ(i)−X
i
ν(i) = 1 −1 = 0.
B={i∈F, θ(i)≥0}
Bc={i∈F, θ(i)<0}
θ(B) = Pi∈Bθ(i)
θ(Bc) = Pi∈Bcθ(i)
b
θ=θ·Qb Bb Bc
kθk=θ(B)
d(µ, ν) = kµ−νkd
kb θk=b θ(b B)
=X
j∈
b
Bb
θ(j)
≤X
j∈
b
BX
i∈B
θ(i)qij
≤X
i∈B
θ(i)X
j∈
b
B
qij

a= inf
ij qij a > 0
X
j∈
b
B
qij ≤1−a < 1
kb θk ≤ (1 −a)X
i∈B
θ(i)
kb θk ≤ (1 −a)kθk
0< a < 1
G
X1X2XnG1⊂G
g0∈G
n gn+1 =Xn+1gn
Xi
µ Xi
Xn(...X3(X2(X1g0))...)
θ G
θ G
n= 5
gn+1 =Xn+1gn=⇒Xn+1 =gn+1 g−1
n
=⇒P[gn+1 =j|gn=i] = P£Xn+1 =ji−1|gn=i¤
gnX1...XnXn
P[gn+1 =j|gn=i] = P£Xn+1 =ji−1¤
=µ(ji−1)
=qij

h
(jh)(ih)−1= (jh)(h−1i−1)
=ji−1
∀h∈G, qi,j =qih,jh
θh:i7→ θ(ih)θh
Piθh(i) = Piθ(ih) = 1
θQ =θ=⇒θhQ=θh
θ
∀i, ∀h:θh(i) = θ(ih) = θ(i) =⇒ ∀i, j :θ(i) = θ(j)
θ
XΩ = RX(Ω)
µ X µ(x) = P[X=x]
Z=eitX i2=−1t∈RZ: Ω →C
µbµ
bµ(t) = E£eitX ¤
=E[cos(tX) + isin(tX)]
=X
x∈R
cos(tx)µ(x) + iX
x∈R
sin(tx)µ(x)
∀θ, µ :b θ(t) = bµ(t)⇐⇒ θ=µ
X1...Xnn
µ1...µnSn=X1+... +Xnν Sn
bν(t) = cµ1(t)×cµ2(t)×... ×cµn(t)
ea+b=eaeb
∀j, µj=µbν(t) = bµ(t)n

(Xj)j
µ σ2X1Xn=X1+... +Xn
n(Xn)n
m=E[X1] = X
x
xµ(x)
P·a≤√nXn−m
σ≤b¸n→∞
−→ 1
2πZb
a
e−x2
2dx
n≥12