
Introduction to Stochastic Processes [pdf] - m4rtyr
https://web.ma.utexas.edu/users/gordanz/notes/introduction_to_stochastic_processes.pdf
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jcreinhold
I took this class a few years ago. Prof. Žitković is a fantastic teacher.

There is a set of more recent lecture notes here,
[https://web.ma.utexas.edu/users/gordanz/lecture_notes_page.h...](https://web.ma.utexas.edu/users/gordanz/lecture_notes_page.html),
under the "Introduction to Stochastic Processes" section, FYI.

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ves
seconded, his grad probability classes were some of my favorites a few years
ago (also hi!).

Measure theoretic probability significantly influenced how I think about
nearly everything today, which is as strong an endorsement of these notes as I
can muster.

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eachro
Just out of curiousity, can you say a bit about how it influences your every
day thinking? And why is measure theory so essential to really understanding
probability? I sort of understand why it's necessary to have the language of
measure theory and be able to talk about the measures/probabilities of
uncountable sets but don't really understand beyond that. I have the
equivalent of an undergrads understanding of measure theory after numerous gos
at it but I haven't ever been able to piece it all together to have a cohesive
understanding of the area the way I do for say linear algebra.

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FabHK
> can you say a bit about how it influences your every day thinking?

yes, I'd like to hear about that, too. I took Theory of Probability classes,
and I appreciate that some complicated stuff is necessary to avoid some neat
paradoxes, but must admit that measure theory hasn't taken my thinking or
intuition forward at all.

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siddboots
Prior to giving real analysis and measure theory a serious go, I feel as
though I was carrying around quite a lot of notation baggage that was
essentially opaque to me. A lot of it was simply "received knowledge" and not
at all cleanly organized in my mind.

For example, I remember fumbling over a modelling problem involving mixed
random variables (that is, random variables with both continuous and discrete
parts), and in retrospect the problem was that I just didn't have a clear
understanding of what a random variable is, and how it relates to mathematical
objects and concepts that I was more familiar with, like functions and vector
spaces.

The point, for me, was not about needing to use the language of sigma-algebras
to solve the types of problems that I come across in my job (electrical
engineering and data analysis). It was more about going through the exercise
of constructing the tools that I was using day-to-day, so that I could
manipulate them with more confidence and creativity.

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throwawaySG
Do you think that real analysis and measure theory helped you get a better
grip on the notion of a r.v. than just the simple function from sample space
to real line definition? I'm slightly tempted to take or at least try to self-
study real analysis and eventually measure theory, but everyone I know
(including profs) has told me not to bother if I'm not going to do theoretical
stuff.

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nicolapede
It depends what you mean by "getting a better grip". There are books on
scientific topics that do not rely on technical details. When they are great,
they are so exactly because, even with this constraint, they manage to clearly
convey the elemental notions to a layman ([0] is a great example). It is
debatable whether the grip you get in this way is better or not. Certainly it
can get deeper, when complemented with the right analytical tools.

[0] - [https://www.amazon.co.uk/Relativity-Routledge-Classics-
Bertr...](https://www.amazon.co.uk/Relativity-Routledge-Classics-Bertrand-
Russell/dp/0415473829)

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nathell
This is the first non-Polish mathematical text I’ve seen that’s typeset in
Torunian Antiqua [1], one of my favourite font faces.

[1]: [https://jmn.pl/pliki/AntykwaTorunska-doc-
en.pdf](https://jmn.pl/pliki/AntykwaTorunska-doc-en.pdf)

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fouc
Makes me think of Harry Potter

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throwlaplace
these notes are typeset using mathematica. does anyone have a guide for
typesetting mathematica notebooks this way? they're the best example of using
mathematica to typeset i've ever seen

