Stochastische Analysis by Wolfgang Hackenbroch- Bookswagon UAE
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Stochastische Analysis

Stochastische Analysis


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About the Book

Dieses Buch will in das Gebiet der "Stochastischen Analysis" einführen. Was ist unter dieser Begriffsverbindung zu verstehen? Würde man die Stochastik beiseite lassen und nur den deterministischen Spezialfall der Theorie betrachten, so bliebe ein Stück klassischer Analysis für Funktionen einer reellen Variablen, vor allem Grenzwerttheorie, Differential- und Integralrechnung und die Theorie gewöhnli- cher Differentialgleichungen. Nimmt man aber eine geeignete Zufallsabhängigkeit hinzu, so eröffnet sich ein moderner Zweig der Theorie der Stochastischen Prozesse mit neuartigen rechnerischen Möglichkeiten und unerwarteten Einsichten. Diese beschränken sich keineswegs auf stochastische Zusammenhänge, etwa ein tieferes Verständnis der Brownschen Bewegung und ihrer fundamentalen Rolle in der Be- schreibung von Fluktuationsphänomenen. Vielmehr erlaubt die Einbeziehung des Zufalls als eines weiteren Freiheitsgrades in die Analysis Brückenschläge zu an- deren Gebieten der Mathematik und Mathematischen Physik. So ergeben sich Querverbindungen zwischen partiellen Differentialgleichungen und stochastischen gewöhnlichen Differentialgleichungen; das Studium stochastischer Flüsse auf Man- nigfaltigkeiten ist eng mit deren Geometrie (insbesondere Krümmung) verknüpft; Pfadintegraldarstellungen von Schrödinger-Halbgruppen präzisieren und begrün- den physikalische Betrachtungsweisen von Dirac und Feynman über den Zusam- menhang von klassischer und Quantenmechanik - und vieles andere. Ein kurzes Wort zu den Absichten dieses Textes. Zunächst sei eingestanden, daß unser Ausgangspunkt und damit auch die Argumentationsweise in erster Linie analytisch ist, was bedeuten soll, daß wir im Zweifel etwa einem detaillierten maß- theoretischen oder (im letzten Kapitel) differentialgeometrischen vor einem mehr intuitiven probabilistischen Argument den Vorzug gegeben haben.


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Product Details
  • ISBN-13: 9783519022299
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Edition: 1994 ed.
  • Language: German
  • Returnable: N
  • Spine Width: 29 mm
  • Weight: 942 gr
  • ISBN-10: 351902229X
  • Publisher Date: 01 Jan 1994
  • Binding: Paperback
  • Height: 244 mm
  • No of Pages: 560
  • Series Title: Mathematische Leitfäden
  • Sub Title: Eine Einführung in Die Theorie Der Stetigen Semimartingale
  • Width: 170 mm


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