Generalized Stochastic Processes

Modelling and Applications of Noise Processes

verfasst von: Prof. Stefan Schäffler

Verlag: Springer International Publishing

Buchreihe : Compact Textbooks in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This textbook shall serve a double purpose: first of all, it is a book about generalized stochastic processes, a very important but highly neglected part of probability theory which plays an outstanding role in noise modelling. Secondly, this textbook is a guide to noise modelling for mathematicians and engineers to foster the interdisciplinary discussion between mathematicians (to provide effective noise models) and engineers (to be familiar with the mathematical backround of noise modelling in order to handle noise models in an optimal way).Two appendices on "A Short Course in Probability Theory" and "Spectral Theory of Stochastic Processes" plus a well-choosen set of problems and solutions round this compact textbook off.

Inhaltsverzeichnis

Frontmatter

1. Generalized Functions

Abstract

On the real valued spaces \(\mathbb {R}^n\), \(n \in \mathbb {N}\), we use the Euclidean norm .

Stefan Schäffler

2. Stochastic Processes

Abstract

Let \((\varOmega, {\mathcal {S}}, \mathbb {P})\) be a probability space. Each probability space is a model for a random experiment with a nonempty set Ω of the possible results .

Stefan Schäffler

3. Stochastic Differential Equations

Abstract

Considering the capacitor voltage U _c in an LRC circuit (see ⊡ Fig. 3.1).

Stefan Schäffler

4. Generalized Random Fields

Abstract

Let \((\varOmega , {\mathcal {S}},\mathbb {P})\) be a probability space and let \((H, {\mathcal {H}},\mu )\) be a measure space.

Stefan Schäffler

Backmatter

Titel: Generalized Stochastic Processes
verfasst von: Prof. Stefan Schäffler
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-78768-8
Print ISBN: 978-3-319-78767-1
DOI: https://doi.org/10.1007/978-3-319-78768-8