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Semimartingale Theory and Stochastic Calculus

DOI link for Semimartingale Theory and Stochastic Calculus

Semimartingale Theory and Stochastic Calculus book

Semimartingale Theory and Stochastic Calculus

DOI link for Semimartingale Theory and Stochastic Calculus

Semimartingale Theory and Stochastic Calculus book

Edited BySheng-wu He, Jia-gang Wang, Jia-an Yan
Edition 1st Edition
First Published 1992
eBook Published 17 July 2019
Pub. Location Boca Raton
Imprint Routledge
DOI https://doi.org/10.1201/9780203739907
Pages 400
eBook ISBN 9780203739907
Subjects Mathematics & Statistics
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Wang, J.-G., & Yan, J.-A. (1992). Semimartingale Theory and Stochastic Calculus (S.-W. He, Ed.) (1st ed.). CRC Press. https://doi.org/10.1201/9780203739907

ABSTRACT

Semimartingale Theory and Stochastic Calculus presents a systematic and detailed account of the general theory of stochastic processes, the semimartingale theory, and related stochastic calculus. The book emphasizes stochastic integration for semimartingales, characteristics of semimartingales, predictable representation properties and weak convergence of semimartingales. It also includes a concise treatment of absolute continuity and singularity, contiguity, and entire separation of measures by semimartingale approach. Two basic types of processes frequently encountered in applied probability and statistics are highlighted: processes with independent increments and marked point processes encountered frequently in applied probability and statistics.

Semimartingale Theory and Stochastic Calculus is a self-contained and comprehensive book that will be valuable for research mathematicians, statisticians, engineers, and students.

TABLE OF CONTENTS

chapter I|26 pages

Preliminaries

chapter II|52 pages

Classical Martingale Theory

chapter III|31 pages

Processes and Stopping Times

chapter IV|25 pages

Section Theorems and Their Applications

chapter V|26 pages

Projections of Processes

chapter VI|16 pages

Martingales with Integrable Variation and Square Integrable Martingales

chapter VII|18 pages

Local Martingales

chapter VIII|17 pages

Semimartingales and Quasimartingales

chapter IX|39 pages

Stochastic Integrals

chapter X|28 pages

Martingale Spaces H 1 and BMO

chapter XI|39 pages

The Characteristics of Semimartingales

chapter XII|30 pages

Changes of Measures

chapter XIII|34 pages

Predictable Representation Property

chapter XIV|41 pages

Absolute Continuity and Contiguity of Measures

chapter XV|44 pages

Weak Convergence for Cadlag Processes

chapter XVI|48 pages

Weak Convergence for Semimartingales

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