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Stochastische Matrizen by F. -J Fritz, B. Huppert, W. Willems

Stochastische Matrizen

by F. -J Fritz , B. Huppert , W. Willems
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Book cover type: Paperback
  • ISBN13: 9783540091264
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 196
  • Original Price: EUR 46.72
  • Language: German
  • Edition: N/A
  • Item Weight: 341 grams
  • BISAC Subject(s): Probability & Statistics / General

In der Anfängervorlesung "Lineare Algebra" lernt der Student ein umfang- reiches System von Begriffen und Ergebnissen kennen. Auf die Bedeutung dieser Theorie für die ganz"e t1athematik wird er zwar oft hingewiesen, aber vorgeführt werden meist nur Anwendungen aus der Geometrie. Das vorliegende kleine Heft ist äer Versuch, ein anderes Gebiet für die Motivierung der Anfängervorlesung zu erschlie en, nämlich die Theorie der stochastischen Prozesse mit endl ch vielen Zuständen in matrizen- theoretischer Behandlung. Unsere Darstellung steht zwischen den sehr elementar gehaltenen Büchern (mitunter mit dem Titel "Finite Mathema- tics"), die zum Teil für Nichtmathematiker geschrieben sind und nur Elemente der Linearen Algebra verwenden, und den allgemeinen Theorien der stochastischen Prozesse, welche dem endlichen Spezialfall oft wenig Raum widmen. Sie stützt sich weitgehend auf die Betrachtung der Eigen- werte von stochastischen Matrizen. Obwohl die Bestimmung der Eigenwerte nicht direkt ein Teil des Problems ist, scheint uns das Studium der Eigenwerte den besten Aufschlu über das Verhalten der Potenzen einer stochastischen Matrix zu geben. (Wir sind uns dessen bewu t, da diese Methode freilich für stochastische Prozesse mit unendlich vielen Zustän- den völlig versagt. ) Nach der Erörterung der Problemstellung und einigen Beispielen in 1 werden in 2 alle später benötigten Aussagen über die Eigenwerte von stochastischen Matrizen hergeleitet. Darauf folgen dann in 3 leicht die Konvergenzsätze. In 4 behandeln wir weitere Sätze über die Eigen- werte von stochastischen Matrizen, die jedoch später kaum mehr verwen- det werden.

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