The Contraction Method on C([0,1]) and Donsker's ... - Eurandom

<strong>The</strong> Zolotarev metric on C([0, 1])
Let M(C([0, 1])) be the set of probability measures on C([0, 1]).
For µ, ν ∈ M(C([0, 1])) and s > 0 define the Zolotarev distance of
µ and ν by
ζs(µ, ν) = sup |E[f (X ) − f (Y )]|,
f ∈Fs
with L(X ) = µ, L(Y ) = ν and for s = m + α with 0 < α ≤ 1 and
m := ⌈s⌉ − 1 ∈ N0
Fs := {f ∈ C m (C([0, 1]), R) : D m f (x)−D m f (y) ≤ x−y α , x, y ∈ C(
Set ζs(X , Y ) = ζs(L(X ), L(Y )).
Henning Sulzbach J. W. Goethe-Universität Frankfurt a. M. <strong>The</strong> <strong>Contraction</strong> <strong>Method</strong> on C([0, 1]) and Donsker’s <strong>The</strong>orem