Foundations of Infinitesimal Stochastic Analysis

1st Edition

Authors: K.D. Stroyan J.M. Bayod
Hardcover ISBN: 9780444879271
eBook ISBN: 9780080960425
Imprint: North Holland
Published Date: 1st January 1986
24.95 + applicable tax
14.99 + applicable tax
18.95 + applicable tax
Unavailable
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access


Description

This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

Table of Contents

Preliminary Constructions. Chapters: 1. Finite and Hyperfinite Measures. Limited Hyperfinite Measures. Unlimited Hyperfinite Measures. Measurable and Internal Functions. Hyperfinite Integration. Conditional Expectation. Weak Compactness and SL1. 2. Measures and the Standard Part Map. Lebesgue Measure. Borel and Loeb Sets. Borel Measures. Weak Standard Parts of Measures. 3. Products of Hyperfinite Measures. Anderson's Extension. Hoover's Strict Inclusion. Keisler's Fubini Theorem. 4. Distributions. One Dimensional Distributions. Joint Distributions. Laws and Independence. Some Finite Independent Sums. 5. Paths of Processes. Metric Lifting and Projecting. Continuous Path Processes. Decent Path Processes. Lebesgue and Borel Path Processes. Beyond [0,1] and Scalar Values. 6. Hyperfinite Evolution. Events Determined at Times and Instants. Progressive and Previsible Measurability. Nonanticipating Processes. Measurable and Internal Stopping. Martingales. Predictable Processes. Beyond [0,1] with Localization. 7. Stochastic Integration. Stieltjes Integrals and Variation. Quadratic Variation. Square Martingale Integrals. Toward Local Martingale Integrals. Notes on Continuous Martingales. Stable Martingale Liftings. Semimartingale Integrals. Afterword. References. Index.

Details

Language:
English
Copyright:
© North Holland 1986
Published:
Imprint:
North Holland
eBook ISBN:
9780080960425
Hardcover ISBN:
9780444879271

About the Author

K.D. Stroyan

Affiliations and Expertise

Department of Mathematics, The University of Iowa Iowa City. Iowa

J.M. Bayod