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Introduction to Stochastic Processes [pdf]

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Re: Introduction to Stochastic Processes [pdf]

#4

Post by ves »

jcreinhold wrote: post #2

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... , under the "Introduction to Stochastic Processes" section, FYI.

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.

Re: Introduction to Stochastic Processes [pdf]

#5

Post by eachro »

ves wrote: post #4
jcreinhold wrote: post #2

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... , under the "Introduction to Stochastic Processes" section, FYI.

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.

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.

Re: Introduction to Stochastic Processes [pdf]

#6

Post by FabHK »

eachro wrote: post #5
ves wrote: post #4

Earlier quoted context omitted.

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.

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 meas…

> 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.

Re: Introduction to Stochastic Processes [pdf]

#7

Post by fyp »

ves wrote: post #4
jcreinhold wrote: post #2

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... , under the "Introduction to Stochastic Processes" section, FYI.

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.

I struggled through graduate analysis and measure theory as prereqs just to get to measure theoretic probability.

But I didn't retain much since it wasn't good for building intuition (informal proofs were better for that) and a lot of the corner cases it fixed didn't matter for the real world.

The language of measure theory makes a lot of proofs much shorter and easier to remember though. For example, markov's inequality: https://en.wikipedia.org/wiki/Markov%27s_inequality#In_the_l...

Re: Introduction to Stochastic Processes [pdf]

#8

Post by siddboots »

FabHK wrote: post #6
eachro wrote: post #5

Earlier quoted context omitted.

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 meas…

> 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.

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.

Re: Introduction to Stochastic Processes [pdf]

#9

Post by throwawaySG »

siddboots wrote: post #8
FabHK wrote: post #6

Earlier quoted context omitted.

> 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.

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), an…

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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