Encyclopaedia of Mathematical Sciences

Probability Theory III

Stochastic Calculus

Editors: Prokhorov, Yurij V., Shiryaev, Albert N. (Eds.)

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About this book

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 ranĀ­ 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.

Table of contents (4 chapters)

  • Introduction to Stochastic Calculus

    Krylov, N. V.

    Pages 7-37

  • Stochastic Differential and Evolution Equations

    Anulova, S. V. (et al.)

    Pages 38-110

  • Stochastic Calculus on Filtered Probability Spaces

    Liptser, R. Sh. (et al.)

    Pages 111-157

  • Martingales and Limit Theorems for Stochastic Processes

    Liptser, R. Sh. (et al.)

    Pages 158-247

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-662-03640-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-3-540-54687-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-3-642-08122-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Probability Theory III
Book Subtitle
Stochastic Calculus
Editors
  • Yurij V. Prokhorov
  • Albert N. Shiryaev
Translated by
Slater, P.B.
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
45
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-03640-2
DOI
10.1007/978-3-662-03640-2
Hardcover ISBN
978-3-540-54687-0
Softcover ISBN
978-3-642-08122-4
Series ISSN
0938-0396
Edition Number
1
Number of Pages
VI, 256
Additional Information
Original Russian edition published by VINITI, Moscow, 1989
Topics