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Inequalities in analysis and probability
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Description
Rating
Title
Inequalities
in
analysis
and
probability
Creator
Pons, Odile.
Contributors
World Scientific (Firm)
DescriptionAbstract
The
book
is
aimed
at
graduate
students
and
researchers
with
basic
knowledge
of
Probability
and
Integration
Theory
.
It
introduces
classical
inequalities
in
vector
and
functional
spaces
with
applications
to
probability
.
It
also
develops
new
extensions
of the
analytical
inequalities
, with
sharper
bounds
and
generalizations
to the
sum
or the
supremum
of
random
variables
, to
martingales
and to
transformed
motions
. The
proofs
of the
new
results
are
presented
in
great
detail
.
DescriptionTable Of Contents
1
.
Preliminaries
.
1.1
.
Introduction
.
1.2
.
Cauchy
and
Holder
inequalities
.
1.3
.
Inequalities
for
transformed
series
and
functions
.
1.4
.
Applications
in
probability
.
1.5
.
Hardy's
inequality
.
1.6
.
Inequalities
for
discrete
martingales
.
1.7
.
Martingales
indexed
by
continuous
parameters
.
1.8
.
Large
deviations
and
exponential
inequalities
.
1.9
.
Functional
inequalities
.
1.10
.
Content
of the
book

2
.
Inequalities
for
means
and
integrals
.
2.1
.
Introduction
.
2.2
.
Inequalities
for
means
in
real
vector
spaces
.
2.3
.
Holder
and
Hilbert
inequalities
.
2.4
.
Generalizations
of
Hardy's
inequality
.
2.5
.
Carleman's
inequality
and
generalizations
.
2.6
.
Minkowski's
inequality
and
generalizations
.
2.7
.
Inequalities
for the
Laplace
transform
.
2.8
.
Inequalities
for
multivariate
functions

3
.
Analytic
inequalities
.
3.1
.
Introduction
.
3.2
.
Bounds
for
series
.
3.3
.
Cauchy's
inequalities
and
convex
mappings
.
3.4
.
Inequalities
for the
mode
and the
median
.
3.5
.
Mean
residual
time
.
3.6
.
Functional
equations
.
3.7
.
Carlson's
inequality
.
3.8
.
Functional
means
.
3.9
.
Young's
inequalities
.
3.10
.
Entropy
and
information

4
.
Inequalities
for
martingales
.
4.1
.
Introduction
.
4.2
.
Inequalities
for
sums
of
independent
random
variables
.
4.3
.
Inequalities
for
discrete
martingales
.
4.4
.
Inequalities
for
martingales
indexed
by
[symbol]
.
4.5
.
Poisson
processes
.
4.6
.
motion
.
4.7
.
Diffusion
processes
.
4.8
.
Level
crossing
probabilities
.
4.9
.
Martingales
in the
plane

5
.
Functional
inequalities
.
5.1
.
Introduction
.
5.2
.
Exponential
inequalities
for
functional
empirical
processes
.
5.3
.
Exponential
inequalities
for
functional
martingales
.
5.4
.
Weak
convergence
of
functional
processes
.
5.5
.
Differentiable
functionals
of
empirical
processes
.
5.6
.
Regression
functions
and
biased
length
.
5.7
.
Regression
functions
for
processes

6
.
Inequalities
for
processes
.
6.1
.
Introduction
.
6.2
.
Stationary
processes
.
6.3
.
Ruin
models
.
6.4
.
Comparison
of
models
.
6.5
.
Moments
of the
processes
at
T[symbol]
.
6.6
.
Empirical
process
in
mixture
distributions
.
6.7
.
Integral
inequalities
in the
plane
.
6.8
.
Spatial
point
processes

7
.
Inequalities
in
complex
spaces
.
7.1
.
Introduction
.
7.2
.
Polynomials
.
7.3
.
Fourier
and
Hermite
transforms
.
7.4
.
Inequalities
for the
transforms
.
7.5
.
Inequalities
in
[symbol]
.
7.6
.
Complex
spaces
of
higher
dimensions
.
7.7
.
Stochastic
integrals
.
Publisher
World Scientific Pub. Co.
Subject
Inequalities (Mathematics)
Probabilities.
Identifier
9789814412582
(electronic
bk.)
;
9789814412575
;
http://www.worldscientific.com/worldscibooks/10.1142/8529#t=toc
Language
eng
Type
Electronic books.
FormatExtent
ix, 221 p. : ill.
Date
c2013
.
OCLC number
874502215
CONTENTdm number
532
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