Levy Processes and Infinitely Divisible Distributions
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Author Description
Levy processes are a class of stochastic processes with independent and stationary increments. They are fundamental to the study of probability and have applications in various fields, including finance, physics, and engineering. Infinitely divisible distributions are closely related to Levy processes, forming the class of distributions that can be represented as the sum of an arbitrary number of independent and identically distributed random variables. This book provides a comprehensive account of the theory of Levy processes and infinitely divisible distributions, covering their basic properties, structure, and applications. It is intended for researchers and graduate students in probability and statistics.
Menrva's Summary
THE THESIS
This book investigates the fundamental properties and applications of Levy processes and infinitely divisible distributions within probability theory. It delves into the intricate mathematical structures that underpin these processes, exploring their theoretical underpinnings and their relevance in modeling complex phenomena. The work is structured to provide a comprehensive understanding for researchers and advanced students in probability and related fields.
THE SCOPE MAP
- Detailed exploration of the theory of Levy processes.
- In-depth analysis of infinitely divisible distributions.
- Discussion of the relationship between Levy processes and their associated distributions.
- Coverage of key concepts such as characteristic functions and semigroups.
- Examination of the structure of Levy processes, including their paths and sample path properties.
- Introduction to related topics like stable processes and their generalizations.
- Presentation of various examples and applications in different scientific domains.
THE AUTHORITY PERSPECTIVE
This text is recognized as a rigorous and comprehensive treatment of Levy processes and infinitely divisible distributions, aimed at a specialized audience within the mathematical sciences. Its depth and theoretical focus suggest it serves as a valuable reference for researchers and graduate students seeking a thorough understanding of these advanced probabilistic concepts. The work is likely to be appreciated for its systematic approach and detailed mathematical exposition.
Page Count:
536
Publication Date:
2013-01-01
ISBN-10:
1107656494
ISBN-13:
9781107656499
Science
Probability Theory
Mathematical Analysis
Stochastic processes
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