Bernstein Functions Theory and Applications

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The wor...

Ausführliche Beschreibung

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Bibliographische Detailangaben
Hauptverfasser: Schilling, René L, Song, Renming, Vondracek, Zoran
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Berlin/Boston De Gruyter 2012
Walter de Gruyter GmbH
Ausgabe:1
Schriftenreihe:De Gruyter Studies in Mathematics
Schlagworte:
Analytic functions
Bernstein Functions
Bernstein-Funktion
Complete Bernstein Functions
Completely Monotone Function
Halbgruppe
Laplace Transform
MATHEMATICS
MATHEMATICS / General
MATHEMATICS / Mathematical Analysis
MATHEMATICS / Probability & Statistics / General
Mathematics. Analysis
monotone Funktion
Monotonic functions
Operatortheorie
Quasianalytic functions
Stieltjes Function/Transform
Wahrscheinlichkeitsmaß
Bernstein-Funktion
Bernstein Functions
Complete Bernstein Functions
Operatortheorie
Wahrscheinlichkeitsmaß
Completely Monotone Function
monotone Funktion
Laplace Transform
Stieltjes Function/Transform
Halbgruppe
ISBN:9783110269338, 3110269333, 3110252295, 9783110252293, 3110215314, 9783110215311, 3110215306, 9783110215304
Online-Zugang:Volltext
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Inhaltsangabe:
  • Frontmatter -- Contents -- 1 Completely monotone functions -- 2 Stieltjes functions -- 3 Bernstein functions -- 4 Positive and negative definite functions -- 5 A probabilistic intermezzo -- 6 Complete Bernstein functions: representation -- 7 Complete Bernstein functions: properties -- 8 Thorin-Bernstein functions -- 9 A second probabilistic intermezzo -- 10 Special Bernstein functions and potentials -- 11 The spectral theorem and operator monotonicity -- 12 Subordination and Bochner's functional calculus -- 13 Potential theory of subordinate killed Brownian motion -- 14 Applications to generalized diffusions -- 15 Examples of complete Bernstein functions -- Backmatter
  • Intro -- Preface to the second edition -- Preface -- Index of notation -- 1 Completely monotone functions -- 2 Stieltjes functions -- 3 Bernstein functions -- 4 Positive and negative definite functions -- 5 A probabilistic intermezzo -- 6 Complete Bernstein functions -- 6.1 Representation of complete Bernstein functions -- 6.2 Extended complete Bernstein functions -- 7 Properties of complete Bernstein functions -- 8 Thorin-Bernstein functions -- 9 A second probabilistic intermezzo -- 10 Transformations of Bernstein functions -- 11 Special Bernstein functions and potentials -- 11.1 Special Bernstein functions -- 11.2 Hirsch's class -- 12 The spectral theorem and operator monotonicity -- 12.1 The spectral theorem -- 12.2 Operator monotone functions -- 13 Subordination and Bochner's functional calculus -- 13.1 Semigroups and subordination in the sense of Bochner -- 13.2 A functional calculus for generators of semigroups -- 13.3 Subordination and functional inequalities -- 13.4 Eigenvalue estimates for subordinate processes -- 14 Potential theory of subordinate killed Brownian motion -- 15 Applications to generalized diffusions -- 15.1 Inverse local time at zero -- 15.2 First passage times -- 16 Examples of complete Bernstein functions -- 16.1 Special functions used in the tables -- 16.2 Algebraic functions -- 16.3 Exponential functions -- 16.4 Logarithmic functions -- 16.5 Inverse trigonometric functions -- 16.6 Hyperbolic functions -- 16.7 Inverse hyperbolic functions -- 16.8 Gamma and related special functions -- 16.9 Bessel functions -- 16.10 Miscellaneous functions -- 16.11 CBFs given by exponential representations -- 16.12 Additional comments -- Appendix -- A.1 Vague and weak convergence of measures -- A.2 Hunt processes and Dirichlet forms -- Bibliography -- Index
  • Contents --
  • 9 A second probabilistic intermezzo --
  • 3 Bernstein functions --
  • 8 Thorin–Bernstein functions --
  • 7 Complete Bernstein functions: properties --
  • 10 Special Bernstein functions and potentials --
  • 12 Subordination and Bochner’s functional calculus --
  • 4 Positive and negative definite functions --
  • 6 Complete Bernstein functions: representation --
  • 11 The spectral theorem and operator monotonicity --
  • Backmatter
  • 13 Potential theory of subordinate killed Brownian motion --
  • 1 Completely monotone functions --
  • 15 Examples of complete Bernstein functions --
  • Frontmatter --
  • 2 Stieltjes functions --
  • 14 Applications to generalized diffusions --
  • 5 A probabilistic intermezzo --