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Does stochastic calculus require measure theory?
Stochastic calculus is an advanced topic, which requires measure theory, and often several graduate-level probability courses. The most important result in stochastic calculus is Ito’s Lemma, which is the stochastic version of the chain rule.
What should I learn before stochastic calculus?
What you need is a good foundation in probability, an understanding of stochastic processes (basic ones [markov chains, queues, renewals], what they are, what they look like, applications, markov properties), calculus 2-3 (Taylor expansions are the key) and basic differential equations.
What are prerequisites for measure theory?
The typical prerequisite for measure theory is a two-semester real analysis course, a la Rudin or any of its alternatives (I particularly like Pugh’s book). A solid topological background is also a good idea, although you can probably get away with whatever you learned in real analysis.
Do I Need to Know measure theory?
A lot of probabilistic principles can be learned from finite or countable sample spaces, for which essentially no measure theory is required. Ross’s a First Course in Probability can be profitably read without any measure theory.
Do I need to know basic calculus to learn stochastic calculus?
Stochastic calculus relies heavily on martingales and measure theory, so you should definitely have a basic knowledge of that before learning stochastic calculus. Basic analysis also figures prominently, both in stochastic calculus itself (where limit procedures of various kinds appear, as well as the occasional Hilbert or space…
What are the prerequisites for studying stochastic analysis?
What you need is a good foundation in probability, an understanding of stochastic processes (basic ones [markov chains, queues, renewals], what they are, what they look like, applications, markov properties), calculus 2-3 (Taylor expansions are the key) and basic differential equations. Some people here are trying to scare you away.
Is it possible to apply stochastic calculus without knowing mean square limit?
It is certainly possible to apply stochastic calculus and gain an intuitive understanding of what’s going on without knowing the details of a mean square limit or how to prove a function is square integrable in Lp space. After all, it is a tool that first came into being for thermodynamic processes.