Probability Theory, Random Processes and Mathematical Statistics

by Y. Rozanov

Overview

Probability Theory, Theory of Random Processes and Mathematical Statistics are important areas of modern mathematics and its applications. They develop rigorous models for a proper treatment for various 'random' phenomena which we encounter in the real world. They provide us with numerous tools for an analysis, prediction and, ultimately, control of random phenomena. Statistics itself helps with choice of a proper mathematical model (e.g., by estimation of unknown parameters) on the basis of statistical data collected by observations. This volume is intended to be a concise textbook for a graduate level course, with carefully selected topics representing the most important areas of modern Probability, Random Processes and Statistics. The first part (Ch. 1-3) can serve as a self-contained, elementary introduction to Probability, Random Processes and Statistics. It contains a number of relatively sim­ ple and typical examples of random phenomena which allow a natural introduction of general structures and methods. Only knowledge of elements of real/complex analysis, linear algebra and ordinary differential equations is required here. The second part (Ch. 4-6) provides a foundation of Shastic Analysis, gives information on basic models of random processes and tools to study them. Here a familiarity with elements of functional analysis is necessary. Our intention to make this course fast-moving made it necessary to present important material in a form of examples.

Product Details

ISBN-13:	9789401042017
Publisher:	Springer Netherlands
Publication date:	10/14/2012
Series:	Mathematics and Its Applications , #344
Edition description:	Softcover reprint of the original 1st ed. 1995
Pages:	259
Product dimensions:	6.30(w) x 9.45(h) x 0.02(d)

Table of Contents

1. Introductory Probability Theory.- 1. The Notion of Probability.- 2. Some Probability Models.- 3. Random Variables.- 4. Mathematical Expectation.- 5. Correlation.- 6. Characteristic Functions.- 7. The Central Limit Theorem.- 2. Random Processes.- 1. Random Processes with Discrete State Space.- 2. Random Processes with Continuous States.- 3. An Introduction to Mathematical Statistics.- 1. Some Examples of Statistical Problems and Methods.- 2. Optimality of Statistical Decisions.- 4. Basic Elements of Probability Theory.- 1. General Probability Distributions.- 2. Conditional Probabilities and Expectations.- 3. Conditional Expectations and Martingales.- 5. Elements of Shastic Analysis and Shastic Differential Equations.- 1. Shastic Series.- 2. Shastic Integrals.- 3. Shastic Integral Representations.- 4. Shastic Differential Equations.