Generalized Stochastic Processes

1. Front Matter

   Pages i-xv

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2. Generalized Functions

   • Stefan Schäffler

   Pages 1-27

3. Stochastic Processes

   • Stefan Schäffler

   Pages 29-91

4. Stochastic Differential Equations

   • Stefan Schäffler

   Pages 93-141

5. Generalized Random Fields

   • Stefan Schäffler

   Pages 143-160

6. Back Matter

   Pages 161-183

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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.

• generalized stochastic processes
• noise processes
• circuit simulation
• stochastic integration
• generalized random fields
• generalized random fields
• image processing
• digital communications
• stochastic differential equations

“The book is written with great pedagogical care to serve as an introductory textbook for engineers on the topic of generalized stochastic processes, but it may also represent a valuable reference to a broad audience of researchers who work in the field of stochastic calculus.” (Dora Seleši, zbMATH 1436.60001, 2020)

• Fak. Elektro- und Informationstechnik, Universität der Bundeswehr München, Neubiberg, Germany

  Stefan Schäffler

Prof. Dr. Dr. Stefan Schäffler, University of the Bundeswehr Munich, Faculty of Electrical Engineering and Information Technology, Chair of Mathematics and Operations Research

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