Transportation-information inequalities for Markov processes
In this paper, one investigates the transportation-information T c I inequalities: α ( T c ( ν, μ )) ≤ I ( ν | μ ) for all probability measures ν on a metric space , where μ is a given probability measure, T c ( ν, μ ) is the transportation cost from ν to μ with respect to the cost function c ( x...
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| Published in: | Probability theory and related fields Vol. 144; no. 3-4; pp. 669 - 695 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer-Verlag
01.07.2009
Springer Springer Nature B.V Springer Verlag |
| Subjects: | |
| ISSN: | 0178-8051, 1432-2064 |
| Online Access: | Get full text |
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| Summary: | In this paper, one investigates the transportation-information
T
c
I
inequalities:
α
(
T
c
(
ν, μ
)) ≤
I
(
ν
|
μ
) for all probability measures ν on a metric space
, where
μ
is a given probability measure,
T
c
(
ν, μ
) is the transportation cost from
ν
to
μ
with respect to the cost function
c
(
x
,
y
) on
,
I
(
ν
|
μ
) is the Fisher–Donsker–Varadhan information of ν with respect to
μ
and
α
: [0, ∞) → [0, ∞] is a left continuous increasing function. Using large deviation techniques, it is shown that
T
c
I
is equivalent to some concentration inequality for the occupation measure of a
μ
-reversible ergodic Markov process related to
I
(·|
μ
). The tensorization property of
T
c
I
and comparisons of
T
c
I
with Poincaré and log-Sobolev inequalities are investigated. Several easy-to-check sufficient conditions are provided for special important cases of
T
c
I
and several examples are worked out. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 ObjectType-Feature-2 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0178-8051 1432-2064 |
| DOI: | 10.1007/s00440-008-0159-5 |