# Which courses before Stochastics?

I would like to know which maths course I need to take before studying stochastics.

Thx for helping,

Stephane

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Are you studying it on your own? What kind of stochastics? I see stochastic integrals as tag, then at least measure theory, basic functional analysis and probably some ODE and PDE is necessary. – Jonas Teuwen Sep 15 '11 at 7:06
Yes studying on my own...I mean all kinds of stochastics – Stephane Kouakou Sep 15 '11 at 9:07
measure theory is the essential core of stochastic analysis (as you mentioned stochastic integrals). Generally speaking, to study middle-to-advanced level of stochastics/probability, measure theory is a prerequisite, as far as I experienced. – newbie Sep 15 '11 at 14:31

"All kinds of stochastics" is quite wide formulation, but I guess it includes probability theory (PT). When studying stochastic processes/stochastic calculus/statistics you certainly need to know PT- so I would say this is the basic course here.

Jonas has mentioned measure theory - and it is indeed important for the good understanding of probability (thanks to Kolmogorov's axiomatization) so in some universities students learn measure theory and Lebesgue integrals prior to PT. On the other hand, in many good books on PT the main facts from measure theory are given, so I would say having the separate course in measure is an advantage rather than the necessity.

After PT you can further learn statistics or stochastic processes (they can go almost separately). Again, usually in good books on stochastic processes all necessary facts from other fields (say, topology) are given in appendices. In theory of Markov Chains e.g. you can face a bit of graph theory - but again, it's not necessary to have a separate course on graph theory, the introductory book on shit subject can be sufficient.

If you would like to learn also about Ito calculus, then you have to know how to deal with ODEs and PDEs (again, Jonas has mentioned it). Hope to be useful.

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thx for helping – Stephane Kouakou Sep 15 '11 at 10:08

I would study analysis, linear algebra and probability theory/statistics first as a minimum requirement.

Also, see this question about the prerequisites necessary for the study of probability theory.

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thx for your help – Stephane Kouakou Sep 15 '11 at 10:08

You need to take a first course in probability theory, ending with perhaps the central limit theorem. Perhaps you can start with the the book of Hoel, Port and Stone for introduction to probability, and you can move on the same authors' book on Stochastic processes.

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