Does anyone have a solid road map of what to learn to get to the point where learning stochastic calculus is possible? I have a CS degree that was obtained 8-10 years ago. What are the prerequisites?

A few weeks ago I decided I wanted to get into this so I started self-studying probability theory (with measure theory) [0] as a bridge to start in on stochastic calculus [1]

I think the hardest part of self-studying anything that has some formal math foundations is knowing _what_ to pay attention to. There's so much in just the first chapter of the probability book. Is having a general understanding of set theory enough or should I actually know how to prove a function is a singular function?

That's why I often like to find a university course with lectures posted online so I can use that as a rough guideline for what's important, but I haven't quite found that yet for stochastic calculus. Would love if someone coul point me to one.

[0]: https://www.amazon.com/dp/3030976815 [1]: https://www.amazon.com/dp/9811247560

Same background here. I finally got into stochastic calculus last year thanks to a local college course (after several unsuccessful attempts on my own).

You need at least

1. a basic grasp of classical calculus, measure theory and topology

2. solid understanding of probability theory

3. basics of stochastic processes

I believe you should be able to dive in from there. It's good to have an idea where you're heading as well (mathematical finance and modelling and pricing derivatives? Bayesian inference and MCMC? statistical physics?).

If you want to understand the language of stochastic calculus as mathematicians have formalized it, then you need all of their jargon. Probability, Diff Eqs, Integrals, and Derivatives. If you are trying to tick a box on a resume, then that's what you have to do. If you have a CS degree then you have a little slice of Probability from combinatorics and information theory. You'll have to build up from there.

Stochastic Calculus was invented to understand stochastic processes analytically rather than experimentally. If you just want to build an intuition for stochastic processes, you should skip all that and start playing with Monte Carlo simulations, which you can do easily in Excel, Mathematica, or Python. Other programming languages will work too, but those technologies are the easiest to go from 0 to MC simulation in a short amount of time.

You should learn calculus and differential equations, and then some probability. At that point you should learn a bit of measure theory and then stochastic calculus builds on all that. Stochastic calculus is basically just weird calculus. It has an additional differential dW and the chain rule is more complex (for the Ito formulation. Stratonovich is different but not by much)

From there you study the behavior of various forms of stochastic differential equations that are intended to model certain situations. Then, you make this cool connection between stochastic differential equations and ordinary differential equations that describe the evolution of the corresponding probability distributions. There’s lots of other stuff but those are the hits.

From a CS background, several people I know have raved about the following book[1], of which will be friendly and useful for future needs anyway in the field. The first part of the book is what appears to be a pretty good refresher path.

IMHO working through that book will make you practice with enough basic calc to make moving on to stochastic calculus fairly easy.

[1] Performance Modeling and Design of Computer Systems: Queueing Theory in Action - Mor Harchol-Balter

https://www.cs.cmu.edu/~harchol/PerformanceModeling/book.htm...

There's a book on financial calculus by Rennie and Baxter [0] that gave me very good intuition on the ideas behind option pricing. It starts with the binomial model and moves on to using stochastic calculus. If you get into the topic you'll want to read more in depth books, but this may be a good place to start.

[0] https://www.goodreads.com/book/show/307698.Financial_Calculu...

I'm not a practitioner, so read with some skepticism, but here's my list:

* Calculus

* Real Analysis

* Statistical Mechanics

* Probability

I'm not sure I have any good recommendations for Calculus, but for real analysis, I would recommend "The Way of Analysis" by Strichartz [0].

I don't have good recommendations for books on statistical mechanics, as I haven't found a book that isn't entrenched in coming from a physics perspective and teaches the underlying methods and algorithms. The best I can recommend is "Complexity and Criticality" by Christensen and Moloney [1], but it's pretty far afield of statistical mechanics and the like. Simulating percolation, the Ising model and ricepiles uses a lot of the same methods as financial simulation (MCMC, etc.).

For probability, I would recommend "Probability and Computing" by Mitzenmacher and Upfal [2], "Probability ..." by Durrett [3] and Feller Vol. 1 and 2 [4] [5] for reference.

I also would recommend "Frequently asked questions in Quantitative Finance" by Wilmott [6].

Also know that there's a quantitative finance SO [7] that might be helpful.

[0] https://www.amazon.com/Analysis-Revised-Jones-Bartlett-Mathe...

[1] https://www.amazon.com/COMPLEXITY-CRITICALITY-Imperial-Colle...

[2] https://www.amazon.com/Probability-Computing-Randomization-P...

[3] https://www.amazon.com/Probability-Theory-Examples-Durrett-H...

[4] https://www.amazon.com/Introduction-Probability-Theory-Appli...

[5] https://www.amazon.com/Introduction-Probability-Theory-Appli...

[6] https://www.amazon.com/Frequently-Asked-Questions-Quantitati...

[7] https://quant.stackexchange.com/