## A Basic Course in Probability Theory (2nd Edition)

**Author(s):**

Rabi Bhattacharya, Edward C. Waymire

**Publisher:**

Springer

**Pages:**265

**Further Actions:**

**Categories:**

### AVAILABLE FORMATS

Paperback - 9783319479729

21 February 2017

* $69.99*

**In stock**

Ebook - 9783319479743

13 February 2017

* $54.99*

**In stock**

Quicker paced introduction to the basics allows for a more in-depth treatment of such topics as convergence theory and Brownian motion

Self-contained and suitable for students with varying levels of background in analysis and measure theory

Includes a complete overview of basic measure theory and analysis (with proofs), and an extensive bibliography for further reading in the area

Written in a lively and engaging style

Second edition has additional exercises and expanded basic theory, and a new chapter on general Markov dependent sequences

Preface to First Edition

I. Random Maps, Distribution, and Mathematical Expectation

II. Independence, Conditional Expectation

III. Martingales and Stopping Times

IV. Classical Central Limit Theorems

V. Classical Zero-One Laws, Laws of Large Numbers and Large Deviations

VI. Fourier Series, Fourier Transform, and Characteristic Functions

VII. Weak Convergence of Probability Measures on Metric Spaces

VIII. Random Series of Independent Summands

IX. Kolmogorov's Extension Theorem and Brownian Motion

X. Brownian Motion: The LIL and Some Fine-Scale Properties

XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle

XII. A Historical Note on Brownian Motion

XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium

A. Measure and Integration

B. Topology and Function Spaces

C. Hilbert Spaces and Applications in Measure Theory

References

Symbol Index

Subject Index.