Sheng-Wu He, Jia-Gang Wang, Jia-An Yan

Semimartingale Theory and Stochastic Calculus (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 400
• Erscheinungstermin: 9. Juli 2019
• Englisch
• ISBN-13: 9781351416955
• Artikelnr.: 54910200

Autorenporträt

He Sheng-Wu, Jia-Gang Wang, Jia-an Yan

Inhaltsangabe

PRELIMINARIES. Monotone Class Theorems. Uniform Integrability. Essential
Supremum. The Generalization of Conditional Expectation. Analytic Sets and
Choquet Capacity. Lebesgue-Stieltjes Integrals. CLASSICAL MARTINGALE
THEORY. Elementary Inequalities. Convergence Theorems. Decomposition
Theorems for Supermartingales. Doob's Stopping Theorem. Martingales with
Continuous Time. Processes with Independent Increments. PROCESSES AND
STOPPING TIMES. Stopping Times. Progressive Measurable, Optional and
Predictable Processes. Predictable and Accessible Times. Processes with
Finite Variation. Changes of Time. SECTION THEROREMS AND THEIR
APPLICATIONS. Section Theorems. A.s. Foretellability of Predicatable Times.
Totally Inaccessible Times. Complete Filtrations and the Usual Conditions.
Applications to Martingales. PROJECTIONS OF PROCESSES. Projections of
Measurable Processes. Dual Projections of Increasing Processes.
Applications to Stopping Times and Processes. Doob-Meyer Decomposition
Theorem. Filtrations of Discrete Type. MARTINGALES WITH INTEGRABLE
VARIATION AND SQUARE INTEGRABLE MARTINGALES. Martingales with Integrable
Variation. Stable Subspaces of Square Integrable Martingales. The Structure
of Purely Discontinuous Square Integrable Martingales. Quadratic Variation.
LOCAL MARTINGALES. The Localization of Classes of Processes. The
Decomposition of Local Martingales. The Characterization of Jumps of Local
Martingales. SEMIMARTINGALES AND QUASIMARTINGALES. Semimartingales and
Special Semimartingales. Quasimartingales and Their Rao Decompositions.
Semimartingales on Stochastic Sets of Interval Type. Convergence Theorems
for Semimartingales. STOCHASTIC INTEGRALS. Stochastic Integrals of
Predictable Processes with Respect to Local Martingales. Compensated
Stochastic Integrals of Progressive Processes with Respect to Local
Martingales. Stochastic Integrals of Predictable Processes with Respect to
Semimartingales. Lenglart's Inequality and Convergence Theorems for
Stochastic Inte