# What is filtration?

I am studying Brownian motion and came across the concept of Filtration. However I can't understand how this concept relates to Brownian motion. My notes contained some gibberish about being measurable and adpated. But all these concepts are new to me that I'm having a hard time to grasp what they are about. Can somebody clear that up for me?You should assume that I know nothing about these concepts as I'm totally lost.

• You need a simple example. Have you learned about the binomial asset pricing model?
– whuber
Commented Dec 26, 2013 at 14:51
• @whuber, I did not but will in the future, but read somewhere that Filtration,martingales, etc is the foundation for these types of models
– ankc
Commented Dec 26, 2013 at 16:56
• The nice thing about the binomial asset pricing model is that it does not actually require the machinery of filtrations and martingales to understand or analyze. It can be used to show what those mathematical concepts would actually mean when applied to this simple situation (and their meanings are pretty simple and easy to grasp). The intuition you gain from this exercise can be helpful for studying continuous-time models, where these concepts become essential. Steven Shreve's book is a great resource.
– whuber
Commented Dec 26, 2013 at 16:59
• @whuber, does this stanford.edu/~xing/Stat243/slides_02_bin_model.pdf actually explains the concept of filtration and martingale?
– ankc
Commented Dec 26, 2013 at 17:20
• At stats.stackexchange.com/a/123754/919 I explain and illustrate this in the simplest non-trivial setting.
– whuber
Commented Apr 30, 2022 at 12:46