عنوان
پدید آورنده
موضوع
رده
QA274.75 .U43 2017
QA274
.
75
.
U43
2017
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9789813230927
(Number (ISBN
9813230924
Erroneous ISBN
9789813230910
Erroneous ISBN
9813230916
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Beyond the triangle :
General Material Designation
[Book]
Other Title Information
Brownian motion, Ito calculus, and Fokker-Planck equation : fractional generalizations /
First Statement of Responsibility
by Sabir Umarov (University of New Haven, USA), Marjorie Hahn (Tufts University, USA), Kei Kobayashi (Fordham University, USA).
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New Jersey :
Name of Publisher, Distributor, etc.
World Scientific,
Date of Publication, Distribution, etc.
2017.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
Intro; Contents; Preface; Acknowledgments; 1. Introduction; 1.1 Why fractional generalizations of the Fokker-Planck equation?; 1.2 The problem formulation; 2. The original triangle: Brownian motion, Ito stochastic calculus, and Fokker-Planck-Kolmogorov equation; 2.1 Introduction; 2.2 Brownian motion; 2.3 Ito calculus; 2.4 FPK equations for stochastic processes driven by Brownian motion; 2.4.1 FPK equation associated with Brownian motion; 2.4.2 FPK equations associated with SDEs driven by Brownian motion; 2.4.3 Connection with semigroup theory.
Text of Note
2.4.4 Markovian processes and the Chapman-Kolmogorov equation 2.4.5 FPK equations associated with SDEs driven by Brownian motion in bounded domains; 3. Fractional Calculus; 3.1 The Riemann-Liouville fractional derivative; 3.2 The Caputo-Djrbashian fractional derivative; 3.3 Laplace transform of fractional derivatives; 3.4 Distributed order differential operators; 3.5 The Liouville-Weyl fractional derivatives and the Fourier transform; 3.6 The Riesz potential and the Riesz-Feller fractional derivative; 3.7 Multi-dimensional Riesz potentials and hyper-singular integrals.
Text of Note
4. Pseudo-differential operators associated with Levy processesIntroduction; 4.1 Pseudo-differential operators; 4.2 Pseudo-differential operators with singular symbols; 4.3 Pseudo-differential operators associated with Levy processes; 4.4 Some abstract facts on semigroups and linear operators; 4.5 Pseudo-differential operators on manifolds; 4.6 Pseudo-differential operators associated with stochastic processes in bounded domains; 5. Stochastic processes and time-changes; Introduction; 5.1 The Skorokhod space and its relevant topologies; 5.2 Semimartingales and time-changes; 5.3 Levy processes.
Text of Note
5.4 Subordinators and their inverses5.5 Gaussian processes; 6. Stochastic calculus for time-changed semimartingales and its applications to SDEs; Introduction; 6.1 Stochastic calculus for time-changed semimartingales; 6.2 SDEs driven by time-changed semimartingales; 6.3 CTRW approximations of time-changed processes in the Skorokhod spaces; 6.4 CTRW approximations of time-changed processes in the sense of finite-dimensional distributions; 6.5 Approximations of stochastic integrals driven by time-changed processes; 6.6 Numerical approximations of SDEs driven by a time-changed Brownian motion.
Text of Note
7. Fractional Fokker-Planck-Kolmogorov equationsIntroduction; 7.1 FPK and FPK equations associated with SDEs driven by Brownian motion and Levy processes; 7.2 TFFPK /TDFPK equations associated with SDEs driven by time-changed Levy processes; 7.2.1 Theory; 7.2.2 Applications; 7.3 FPK equations associated with SDEs driven by fractional Brownian motion; 7.3.1 An operator approach to derivation of fractional FPK equations; 7.4 Fractional FPK equations associated with stochastic processes which are time changes of solutions of SDEs driven by fractional Brownian motion; 7.4.1 Theory.
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OTHER EDITION IN ANOTHER MEDIUM
Title
Beyond the triangle.
International Standard Book Number
9789813230910
TOPICAL NAME USED AS SUBJECT
Brownian motion processes.
Fokker-Planck equation.
Stochastic differential equations.
Brownian motion processes.
Fokker-Planck equation.
MATHEMATICS-- Calculus.
MATHEMATICS-- Mathematical Analysis.
Stochastic differential equations.
(SUBJECT CATEGORY (Provisional
MAT-- 005000
MAT-- 034000
DEWEY DECIMAL CLASSIFICATION
Number
515/
.
353
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA274
.
75
Book number
.
U43
2017
PERSONAL NAME - PRIMARY RESPONSIBILITY
Umarov, Sabir
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Hahn, Marjorie G.
Kobayashi, Kei, (Mathematics professor)
ORIGINATING SOURCE
Date of Transaction
20200823231919.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
