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How are ODEs/PDEs/Measure theory introduced in MSQF/FE programs

itsnotbubs

Joined
8/25/23
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Outside of Rutgers and a few other programs ODEs and PDEs aren't a prerequisite. Do FE/QF related graduate programs introduce them and apply them to finance (removing a lot of nuance of the physical application)? The same goes for measure theory, but that is typically a graduate course, though I have not yet seen it as a course at these programs, which I have the same question as before.
 
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No program will cover measure theory. These programs are terminal programs with the main goal of getting their students into good jobs. Thus, the curriculum will never be that rigorous.
 
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To really understand measure theory, 4 year honours undergraduate maths courses are needed. Been there, done that. My Prof was a PhD student of William Feller at Princeton at the the time, so I got it from a good source. terse stuff..

It's kinda cruel subjecting (unprepared) MFE students to MT.

// I always found MT rather lacking in real applications.
 
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Daniel Duffy said:
To really understand measure theory, 4 year honours undergraduate maths courses are needed. Been there, done that. My Prof was a PhD student of William Feller at Princeton at the the time, so I got it from a good source. terse stuff..

It's kinda cruel subjecting (unprepared) MFE students to MT.

// I always found MT rather lacking in real applications.
Click to expand...
Any books you can recommend good sir?
 
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Construction of stochastic integrals is inherently measure theoretic in nature, probability theory done at the graduate level is measure theoretic. While not a formal treatment, Shreve 2 does introduce sigma fields, pointwise convergence almost everywhere, Lebesgue integrals, etc. — basic measure theory topics, sure, but nonetheless it is there.
 
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Qui-Gon said:
Construction of stochastic integrals is inherently measure theoretic in nature, probability theory done at the graduate level is measure theoretic. While not a formal treatment, Shreve 2 does introduce sigma fields, pointwise convergence almost everywhere, Lebesgue integrals, etc. — basic measure theory topics, sure, but nonetheless it is there.
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The treatment is too short..
Do you know the books by Kloeden and Platen? you should.
These are definitive!
 
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I recently tried to learn few pre-requisites with the objective of picking up stochastic calculus.

I found the presentation of the basic ideas in Capinski to be particularly enjoyable - null sets, outer-measure [imath]\mu^{*}(A)[/imath] as the infimum of lengths of all coverings of the set [imath]A[/imath], and that its subadditive. It motivates, that its fair to demand that a length function at the very least be countably additive. All of this just using first principles, just in chapter 2 of the book. Little proofs left as exercises were fulfilling.

Other than that, I understood the key ideas in probability theory - BCL, convergence of RVs from the lecture notes and videos in this playlist.
 
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Just arrived! Handsome bookie for sure.

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Paul Halmos was Hungarian.
I met him a few times at some lectures he gave in the 1970s in Trinity College.

en.wikipedia.org

Paul Halmos - Wikipedia

en.wikipedia.org en.wikipedia.org

  • 1942. Finite-Dimensional Vector Spaces. ...
  • 1950. Measure Theory. ...
  • 1951. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. ...
  • 1956. Lectures on Ergodic Theory. ...
  • 1960. Naive Set Theory. ...
  • 1962. Algebraic Logic. ...
  • 1963. Lectures on Boolean Algebras. ...
  • 1967. A Hilbert Space Problem Book.

The Martians (scientists) - Wikipedia

en.wikipedia.org en.wikipedia.org
 
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Daniel Duffy said:
Paul Halmos was Hungarian.
I met him a few times at some lectures he gave in the 1970s in Trinity College.

en.wikipedia.org

Paul Halmos - Wikipedia

en.wikipedia.org en.wikipedia.org

  • 1942. Finite-Dimensional Vector Spaces. ...
  • 1950. Measure Theory. ...
  • 1951. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. ...
  • 1956. Lectures on Ergodic Theory. ...
  • 1960. Naive Set Theory. ...
  • 1962. Algebraic Logic. ...
  • 1963. Lectures on Boolean Algebras. ...
  • 1967. A Hilbert Space Problem Book.

The Martians (scientists) - Wikipedia

en.wikipedia.org en.wikipedia.org
Click to expand...

I wonder what was in the water in Hungary in those days to produce so many geniuses. :)
 
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Cornelius Lanczos once offered us undergrads a challenge in Dublin; generalise Radon-Nikodym theorem to complex variable case.
 
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