Schilling / Song / Vondracek Bernstein Functions

Theory and Applications
2. revidierte and ext. ed
ISBN: 978-3-11-026933-8
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 37, 424 Seiten

Reihe: De Gruyter Studies in Mathematics

Zielgruppe

Graduate Students, Lecturers, and Researchers in Mathematics; Academic Libraries

Autoren/Hrsg.

Schilling, René L.

Song, Renming

Vondracek, Zoran

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

1;Preface to the second edition;5
2;Preface;6
3;Index of notation;13
4;1 Completely monotone functions;15
5;2 Stieltjes functions;30
6;3 Bernstein functions;35
7;4 Positive and negative definite functions;49
8;5 A probabilistic intermezzo;62
9;6 Complete Bernstein functions;83
9.1;6.1 Representation of complete Bernstein functions;83
9.2;6.2 Extended complete Bernstein functions;94
10;7 Properties of complete Bernstein functions;106
11;8 Thorin-Bernstein functions;123
12;9 A second probabilistic intermezzo;131
13;10 Transformations of Bernstein functions;145
14;11 Special Bernstein functions and potentials;173
14.1;11.1 Special Bernstein functions;173
14.2;11.2 Hirsch’s class;186
15;12 The spectral theorem and operator monotonicity;193
15.1;12.1 The spectral theorem;193
15.2;12.2 Operator monotone functions;201
16;13 Subordination and Bochner’s functional calculus;214
16.1;13.1 Semigroups and subordination in the sense of Bochner;214
16.2;13.2 A functional calculus for generators of semigroups;230
16.3;13.3 Subordination and functional inequalities;247
16.4;13.4 Eigenvalue estimates for subordinate processes;256
17;14 Potential theory of subordinate killed Brownian motion;271
18;15 Applications to generalized diffusions;282
18.1;15.1 Inverse local time at zero;282
18.2;15.2 First passage times;299
19;16 Examples of complete Bernstein functions;313
19.1;16.1 Special functions used in the tables;314
19.2;16.2 Algebraic functions;318
19.3;16.3 Exponential functions;326
19.4;16.4 Logarithmic functions;328
19.5;16.5 Inverse trigonometric functions;344
19.6;16.6 Hyperbolic functions;344
19.7;16.7 Inverse hyperbolic functions;350
19.8;16.8 Gamma and related special functions;354
19.9;16.9 Bessel functions;364
19.10;16.10 Miscellaneous functions;372
19.11;16.11 CBFs given by exponential representations;380
19.12;16.12 Additional comments;385
20;Appendix;388
20.1;A.1 Vague and weak convergence of measures;388
20.2;A.2 Hunt processes and Dirichlet forms;391
21;Bibliography;397
22;Index;420

Über Autor(innen)

Vondracek, Zoran
Zoran Vondra?ek, University of Zagreb, Croatia.

Schilling, René L.
René L. Schilling, Dresden University of Technology, Germany;

Song, Renming
Renming Song, University of Illinois, Urbana, USA;

René L. Schilling, Dresden University of Technology, Germany; Renming Song, University of Illinois, Urbana, USA; Zoran Vondracek, University of Zagreb, Croatia.