
Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions
Lev A. Sakhnovich(Author)
Birkhäuser (Publisher)
Published on 9. August 2014
Book
Paperback/Softback
X, 246 pages
978-3-0348-0801-9 (ISBN)
Description
In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.
More details
Series
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
X, 246 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 15 mm
Weight
394 gr
ISBN-13
978-3-0348-0801-9 (9783034808019)
DOI
10.1007/978-3-0348-0356-4
Schweitzer Classification
Other editions
Additional editions

Lev A. Sakhnovich
Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions
Book
07/2012
1st Edition
Birkhäuser
€90.94
Shipment within 10-15 days

Lev A. Sakhnovich
Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions
E-Book
07/2012
1st Edition
Birkhäuser
€90.94
Available for download
Content
Introduction.- 1 Levy processes.- 2 The principle of imperceptibility of the boundary.- 3 Approximation of positive functions.- 4 Optimal prediction and matched filtering.- 5 Effective construction of a class of non-factorable operators.- 6 Comparison of thermodynamic characteristics.- 7 Dual canonical systems and dual matrix string equations.- 8 Integrable operators and Canonical Differential Systems.- 9 The game between energy and entropy.- 10 Inhomogeneous Boltzmann equations.- 11 Operator Bezoutiant and concrete examples.- Comments.- Bibliography.- Glossary.- Index.