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The Resource From Lévy-Type Processes to Parabolic SPDEs, by Davar Khoshnevisan, René Schilling ; editors for this volume, Lluís Quer-Sardanyons, Frederic Utzet

From Lévy-Type Processes to Parabolic SPDEs, by Davar Khoshnevisan, René Schilling ; editors for this volume, Lluís Quer-Sardanyons, Frederic Utzet

Label
From Lévy-Type Processes to Parabolic SPDEs
Title
From Lévy-Type Processes to Parabolic SPDEs
Statement of responsibility
by Davar Khoshnevisan, René Schilling ; editors for this volume, Lluís Quer-Sardanyons, Frederic Utzet
Creator
Contributor
Author
Author
Editor
Editor
Subject
Language
eng
Summary
This volume presents the lecture notes from two courses given by Davar Khoshnevisan and René Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis. René Schilling's notes are an expanded version of his course on Lévy and Lévy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Lévy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Lévy-Itô decomposition. On the other, it identifies the infinitesimal generator of the Lévy process as a pseudo-differential operator whose symbol is the characteristic exponent of the process, making it possible to study the properties of Feller processes as space inhomogeneous processes that locally behave like Lévy processes. The presentation is self-contained, and includes dedicated chapters that review Markov processes, operator semigroups, random measures, etc. In turn, Davar Khoshnevisan's course investigates selected problems in the field of stochastic partial differential equations of parabolic type. More precisely, the main objective is to establish an Invariance Principle for those equations in a rather general setting, and to deduce, as an application, comparison-type results. The framework in which these problems are addressed goes beyond the classical setting, in the sense that the driving noise is assumed to be a multiplicative space-time white noise on a group, and the underlying elliptic operator corresponds to a generator of a Lévy process on that group. This implies that stochastic integration with respect to the above noise, as well as the existence and uniqueness of a solution for the corresponding equation, become relevant in their own right. These aspects are also developed and supplemented by a wealth of illustrative examples
Member of
Cataloging source
UPM
http://library.link/vocab/creatorName
Khoshnevisan, Davar
Dewey number
519.2
Illustrations
illustrations
Index
index present
LC call number
QA274.2
LC item number
.K476 2016
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Schilling, René L.
  • Quer-Sardanyons, Lluis
  • Utzet, Frederic
Series statement
Advanced Courses in Mathematics : CRM Barcelona,
http://library.link/vocab/subjectName
  • Stochastic analysis
  • Lévy processes
  • Stochastic partial differential equations
  • Mathematics
  • Probability Theory and Stochastic Processes
  • Partial Differential Equations
Label
From Lévy-Type Processes to Parabolic SPDEs, by Davar Khoshnevisan, René Schilling ; editors for this volume, Lluís Quer-Sardanyons, Frederic Utzet
Instantiates
Publication
Copyright
Antecedent source
mixed
Bibliography note
Includes bibliographical references (pages 123-126, 213-216) and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • 4.
  • On the MarkovProperty
  • 5.
  • A Digression: Semigroups
  • 6.
  • The Generator of a Lévy Process
  • 7.
  • Construction of Lévy Processes
  • 8.
  • Two Special Lévy Processes
  • PART I.
  • 9.
  • Random Measures
  • 10.
  • A Digression: Stochastic Integrals
  • 11.
  • From Lévy to Feller Processes
  • 12.
  • Symbols and Semimartingales
  • 13.
  • Dénouement
  • AN INTRODUCTION TO LÉVY AND FELLER PROCESSES
  • Appendix.
  • Some Classical Results
  • 1.
  • Orientation
  • 2.
  • Lévy Processes
  • 3.
  • Examples
  • 14.3.
  • 19.2.3.
  • Example: spatially-homogeneous covariance.
  • 19.2.4.
  • Example: tensor-product covariance.
  • 19.3.
  • Linear SPDEs with colored-noise forcing
  • White noise on G.
  • 14.4.
  • Space-time white noise.
  • 14.5.
  • TheWalsh stochastic integral.
  • 14.5.1.
  • Simple randomfields.
  • 14.5.2.
  • Elementary randomfields.
  • PART II.
  • 14.5.3.
  • Walsh-integrable randomfields.
  • 14.6.
  • Moment inequalities.
  • 14.7.
  • Examples of Walsh-integrable random fields.
  • 14.7.1.
  • Integral kernels.
  • 14.7.2.
  • Stochastic convolutions.
  • INVARIANCE AND COMPARISON PRINCIPLES FOR PARABOLIC STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
  • 14.7.3.
  • Relation to Itô integrals
  • 15.
  • Lévy Processes.
  • 15.1.
  • Introduction.
  • 15.1.1.
  • Lévy processes on R.
  • 15.1.2.
  • Lévy processes on T.
  • 14.
  • 15.1.3.
  • Lévy processes on Z.
  • 15.1.4.
  • Lévy processes on Z/nZ.
  • 15.2.
  • The semigroup.
  • 15.3.
  • The Kolmogorov-Fokker-Planck equation.
  • 15.3.1.
  • Lévy processes on R
  • White Noise..
  • 16.
  • SPDEs.
  • 16.1.
  • A heat equation.
  • 16.2.
  • A parabolic SPDE.
  • 16.2.1.
  • Lévy processes on R.
  • 16.2.2.
  • Lévy processes on a denumerable LCA group.
  • 14.1.
  • 16.2.3.
  • Proof of Theorem 16.2.2.
  • 16.3.
  • Examples.
  • 16.3.1.
  • The trivial group.
  • 16.3.2.
  • The cyclic group on two elements.
  • 16.3.3.
  • The integer group.
  • Some heuristics.
  • 16.3.4.
  • The additive reals.
  • 16.3.5.
  • Higher dimensions
  • 17.
  • An Invariance Principle for Parabolic SPDEs.
  • 17.1.
  • A central limit theorem.
  • 17.2.
  • A local central limit theorem.
  • 14.2.
  • 17.3.
  • Particle systems
  • 18.
  • Comparison Theorems.
  • 18.1.
  • Positivity.
  • 18.2.
  • The Cox-Fleischmann-Greven inequality.
  • 18.3.
  • Slepian's inequality
  • LCA groups.
  • 19.
  • A Dash of Color.
  • 19.1.
  • Reproducing kernel Hilbert spaces.
  • 19.2.
  • Colored noise.
  • 19.2.1.
  • Example: white noise.
  • 19.2.2.
  • Example: Hilbert-Schmidt covariance.
Dimensions
unknown
Extent
1 online resource (viii, 219 pages)
File format
multiple file formats
Form of item
online
Isbn
9783319341200
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-34120-0
Other physical details
illustrations (some color)
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
ocn971059311
Label
From Lévy-Type Processes to Parabolic SPDEs, by Davar Khoshnevisan, René Schilling ; editors for this volume, Lluís Quer-Sardanyons, Frederic Utzet
Publication
Copyright
Antecedent source
mixed
Bibliography note
Includes bibliographical references (pages 123-126, 213-216) and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • 4.
  • On the MarkovProperty
  • 5.
  • A Digression: Semigroups
  • 6.
  • The Generator of a Lévy Process
  • 7.
  • Construction of Lévy Processes
  • 8.
  • Two Special Lévy Processes
  • PART I.
  • 9.
  • Random Measures
  • 10.
  • A Digression: Stochastic Integrals
  • 11.
  • From Lévy to Feller Processes
  • 12.
  • Symbols and Semimartingales
  • 13.
  • Dénouement
  • AN INTRODUCTION TO LÉVY AND FELLER PROCESSES
  • Appendix.
  • Some Classical Results
  • 1.
  • Orientation
  • 2.
  • Lévy Processes
  • 3.
  • Examples
  • 14.3.
  • 19.2.3.
  • Example: spatially-homogeneous covariance.
  • 19.2.4.
  • Example: tensor-product covariance.
  • 19.3.
  • Linear SPDEs with colored-noise forcing
  • White noise on G.
  • 14.4.
  • Space-time white noise.
  • 14.5.
  • TheWalsh stochastic integral.
  • 14.5.1.
  • Simple randomfields.
  • 14.5.2.
  • Elementary randomfields.
  • PART II.
  • 14.5.3.
  • Walsh-integrable randomfields.
  • 14.6.
  • Moment inequalities.
  • 14.7.
  • Examples of Walsh-integrable random fields.
  • 14.7.1.
  • Integral kernels.
  • 14.7.2.
  • Stochastic convolutions.
  • INVARIANCE AND COMPARISON PRINCIPLES FOR PARABOLIC STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
  • 14.7.3.
  • Relation to Itô integrals
  • 15.
  • Lévy Processes.
  • 15.1.
  • Introduction.
  • 15.1.1.
  • Lévy processes on R.
  • 15.1.2.
  • Lévy processes on T.
  • 14.
  • 15.1.3.
  • Lévy processes on Z.
  • 15.1.4.
  • Lévy processes on Z/nZ.
  • 15.2.
  • The semigroup.
  • 15.3.
  • The Kolmogorov-Fokker-Planck equation.
  • 15.3.1.
  • Lévy processes on R
  • White Noise..
  • 16.
  • SPDEs.
  • 16.1.
  • A heat equation.
  • 16.2.
  • A parabolic SPDE.
  • 16.2.1.
  • Lévy processes on R.
  • 16.2.2.
  • Lévy processes on a denumerable LCA group.
  • 14.1.
  • 16.2.3.
  • Proof of Theorem 16.2.2.
  • 16.3.
  • Examples.
  • 16.3.1.
  • The trivial group.
  • 16.3.2.
  • The cyclic group on two elements.
  • 16.3.3.
  • The integer group.
  • Some heuristics.
  • 16.3.4.
  • The additive reals.
  • 16.3.5.
  • Higher dimensions
  • 17.
  • An Invariance Principle for Parabolic SPDEs.
  • 17.1.
  • A central limit theorem.
  • 17.2.
  • A local central limit theorem.
  • 14.2.
  • 17.3.
  • Particle systems
  • 18.
  • Comparison Theorems.
  • 18.1.
  • Positivity.
  • 18.2.
  • The Cox-Fleischmann-Greven inequality.
  • 18.3.
  • Slepian's inequality
  • LCA groups.
  • 19.
  • A Dash of Color.
  • 19.1.
  • Reproducing kernel Hilbert spaces.
  • 19.2.
  • Colored noise.
  • 19.2.1.
  • Example: white noise.
  • 19.2.2.
  • Example: Hilbert-Schmidt covariance.
Dimensions
unknown
Extent
1 online resource (viii, 219 pages)
File format
multiple file formats
Form of item
online
Isbn
9783319341200
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-34120-0
Other physical details
illustrations (some color)
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
ocn971059311

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