Essay on Probability Theory, Machine Learning and Stock Markets. Sorry to bother you, and I'm not entirely sure this is the correct place to be discussing this but I shall try to be brief. 
I'm a complete rookie when it comes to anything stochastic/probability based - I only have an undergraduate course in measure theory under my belt with beginner level courses in Python. However, I'd like to write a thesis on applying techniques from probability theory (Brownian motion/stochastic calculus) with the help of some language such as R/Python in order to look at ways to analyze the "stock market". I understand that each term is in itself a wealth of information, but if someone could either direct me towards papers or any literature so that I could refer to what is being done in the field at the current time.
Ideally, I'd like my project to consist of a mathematical content corresponding to that of an advanced undergraduate/beginning graduate student and involve techniques from machine learning to analyse the data sets. The project itself need not be a testament of originality, but anything, even expository is fine. 
Sorry for the babble, and I wish you all a good day. Thank you.
~ Always.

I think I know what you are after, having crossed that bridge myself. Analyzing the stock market is an interesting thing of itself but tread carefully before you think you have a model that will try and predict the stock prices. Here is a large document that talks about modelling high frequency trades. That said, its also a great opportunity to learn time series modeling, probability theory and pattern recognition. Those skills will help you regardless. Here is a collection of books you could buy from. Hope that helps
