Appendix: Stochastic Processes

Jan H. van Schuppen*

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific


Specialized topics on the theory of stochastic processes are described which are used in the body of this book. Defined are a filtration and stochastic processes relative to a filtration. Elementary martingale theory is discussed. Stopping times and a stochastic process indexed by a stopping time are defined. The supermartingale convergence theorem is established. A brief introduction to ergodicity is provided.

Original languageEnglish
Title of host publicationControl and System Theory of Discrete-Time Stochastic Systems
Number of pages15
ISBN (Electronic)978-3-030-66952-2
Publication statusPublished - 2021

Publication series

NameCommunications and Control Engineering
ISSN (Print)0178-5354
ISSN (Electronic)2197-7119


  • Filtration
  • Martingale
  • Stochastic process
  • Stopping time


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