Semimartingales and their Statistical Inference

B.L.S. Prakasa Rao

• Publisher: CRC Press
• Year: 2019
• Print ISBN: 9781584880080
• eBook ISBN: 9781351416924
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability.
The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales.

Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include:

Asymptotic likelihood theory

Quasi-likelihood

Likelihood and efficiency

Inference for counting processes

Inference for semimartingale regression models

The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• Preface
• Dedication Page
• 1 Semimartingales
• 2 Exponential Families of Stochastic Processes
• 3 Asymptotic Likelihood Theory
• 4 Asymptotic Likelihood Theory for Diffusion Processes with Jumps
• 5 Quasi Likelihood and Semimartingales
• 6 Local Asymptotic Behavior of Semimartingale Experiments
• 7 Likelihood and Asymptotic Efficiency
• 8 Inference for Counting Processes
• 9 Inference for Semimartingale Regression Models
• 10 Applications to Stochastic Modeling
• A Doléans Measure for Semimartingales and Burkholder’s Inequality for Martingales
• B Interchanging Stochastic Inte gration and Ordinary Differentiation and Fubini-Type Theorem for Stochastic Integrals
• C The Fundamental Identity of Sequential Analysis
• D Stieltjes-Lebesgue Calculus
• E A Useful Lemma
• F Contiguity
• G Notes
• Index