# Brownian motion introduction

I didn't get any answers to my previous question; so I am trying a different tack.

I am familiar with a first course in probability theory using measure theory, to the extent of proving the Central Limit Theorem. As a next step I would like to know the basics about Brownian motion, for example to understand one-dimensional Brownian motion in $\mathbb R$, and to be able to use the concept of Wiener measure on the path space, not just the definition, but to use it to prove interesting results, such as the Central limit theorem as mentioned in my previous question.

So, what is a suitable introductory book to Brownian motion for someone familiar with basics of probability? The reference need not prove the CLT as I had asked earlier; but if it does it will be a nice addition.

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try this link.. i've never inspecetd it completely 'cause i just needed some references from time to time.. however here you are... P.S. i'm afraid there is no reference about CLT in it :) stat.berkeley.edu/~peres/bmbook.pdf –  uforoboa Sep 8 '11 at 9:12

## 2 Answers

A basic reference would be

• Zdzislaw Brzezniak, Tomasz Zastawniak: "Basic Stochastic Processes"

starting with the explanation of sigma algebras and conditional expectation. A more advanced and somewhat "canonical" reference is

• Ioannis Karatzas, Steven E. Shreve: "Brownian Motion and Stochastic Calculus".
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Brownian Motion-Peter Mörters and Yuval Peres

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