Probability Theory III: Stochastic Calculus .

Prokhorov, Yu.V. / Shiryaev, A.N. (Eds.).

ISBN 10: 3540546871 / ISBN 13: 9783540546870

Published by Berlin/Heidelberg, Publishers: Springer, 1998., 1997

About this Item

Gr.-8°. 253 Pages. Original Hardcover-Volume. Very good Condition with only minimal Signs of Usage at the Cover. No Markings in the Text! No Underlinings! No Owner's Note! (Encyclopaedia of Mathematical Sciences, 45).

Seller Inventory # 46917BB

Bibliographic Details

• Title: Probability Theory III: Stochastic Calculus .
• Publisher: Berlin/Heidelberg, Publishers: Springer, 1998.
• Publication Date: 1997
• Language: English
• ISBN 10: 3540546871
• ISBN 13: 9783540546870
• Binding: Hardcover
• Seller catalogs:
  • Mathematik - Mathematics

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.