Shiryaev · Probability

Overview

Title	Probability (GTM 95)
Author	Albert N. Shiryaev (А. Н. Ширяев)
Level	Graduate; requires solid analysis background

Why Shiryaev?

Shiryaev’s Probability is a classic in the Springer GTM series and the standard reference for measure-theoretic probability:

• Builds a rigorous, axiomatic foundation from Kolmogorov’s axioms
• Covers classical limit theorems (LLN, CLT, law of the iterated logarithm) in depth
• Strong treatment of random processes — random walks, martingales, Markov chains
• Exercises are thoughtfully designed, with connections to mathematical finance and statistical inference
• The bridge from undergraduate probability to graduate stochastic calculus

Shiryaev assumes comfort with $\sigma$-algebras, measures, and Lebesgue integration. Working through Folland or an equivalent real analysis text in parallel is highly recommended — the two reinforce each other.

Exercises by Chapter

• Chapter 1 · Elementary Probability Theory — Browse →
• Chapter 2 · Mathematical Foundations of Probability Theory — Browse →
• Chapter 3 · Convergence of Probability Measures and the CLT — Browse →

Solutions are added as I work through the text.