De Branges' Theory for Processes with Stationary Increments

Erscheinungsjahr 2026
ISBN: 978-3-032-24845-9
Verlag: Springer Nature Switzerland AG

Buch, Englisch, 781 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Progress in Probability

This monograph explores de Branges’ Hilbert space theory for entire functions and its application to spectral analysis of stationary processes and processes with stationary increments. Chapters examine the interplay between two areas of mathematics: functional analysis and probability theory. These distinct areas are made accessible to readers from either background by establishing the necessary analytic framework in Parts I and II before showing how they apply to Gaussian stochastic processes in Part III. Part I introduces fundamental notions and facts from the complex function theory on a half-plane, including de Branges functions, and Part II focuses on de Branges’ theory. Part III covers spectral analysis of random processes, providing a deeper analysis of moving average representation of processes with stationary increments, their series expansion, and more. will be of interest to researchers in function theory as well as stochastic processes.

Zielgruppe

Research

Autoren/Hrsg.

Dzhaparidze, Kacha

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

I. Functions on a half-place.- 1. Function theory on a half-plane.- 2. De Branges matrix valued functions.- 3. Local operators on Fourier transforms.- II. De Branges spaces of entire functions.- 4. De Branges spaces.- 5. Spaces generated by de Branges matrices.- 6. Chain of spaces.- 7. Spectral measures.- 8. Expansion theorem.- III. Stochastic processes with stationary increments.- 9. Stochastic processes.- 10. Fundamental martingales and Moving average.- 11. Orthogonal series, Karhunen-Loeve expansion.- 12. Isotropic fields with homogeneous increments.