Probability Theory III Stochastic Calculus

Beitr. v. Anulova, S. V., A. Y Veretennikov and N. V Krylov:

ISBN 10: 3540546871 / ISBN 13: 9783540546870

Published by Berlin Springer-Verlag GmbH, 1997

About this Item

VI, 254 S. Neu; Originalverpackt! Versandfertig am nächsten Tag; Rechnung mit MwSt. liegt bei! This volume of the Encyclopaedia is a survey of stochastic calculus which has become an increasingly important part of probability. The topics covered include Brownian motion, the Ito integral, stochastic differential equations and Malliavin calculus, the Sprache: Englisch Gewicht in Gramm: 520.

Seller Inventory # 12441

Bibliographic Details

• Title: Probability Theory III Stochastic Calculus
• Publisher: Berlin Springer-Verlag GmbH
• Publication Date: 1997
• Language: English
• ISBN 10: 3540546871
• ISBN 13: 9783540546870
• Binding: gebundene Ausgabe
• Edition: 1998.
• Condition: Neu
• Weight: 520 grams
• Seller catalogs:
  • Mathematik

About this title

Synopsis

Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth. Theories of processes with independent increments, Markov processes, stationary processes, among others, have been constructed. In the formation and development of the theory of random processes, a significant event was the realization that the construction of a "general theory of ran­ dom processes" requires the introduction of a flow of a-algebras (a filtration) F = (Ftk::o supplementing the triple (n, F, P), where F is interpreted as t the collection of events from F observable up to time t.