Jump to content
Urch Forums

MWG

1st Level
  • Posts

    99
  • Joined

  • Days Won

    2

Everything posted by MWG

  1. Quote begins: Mathematicians prove equivalencies. Because A holds -> B holds, etc. To be honest, I don't consider their 'theorems' to be 'theories'. Also, mathematics doesn't have theories in a Popperian sense. The axioms are, per definition, assumed. This makes the 'theorems' completely insulated. What is then the difference with Freud's theory of the subconscious? Quote ends. Alrite...if you insist to reason in this way... 1. Mathematics is all about equivalence?..... Then John nash's 28 pages of equaivalent relations are certianly not Game "Theory" and his few lines of Galois extention were just unneccessary formalization, and will not lead to your so called "goal". (but Nobel committee had a lower definition of goal than you do) Then Martingale "theorems" are a collection of mathematics "equivalences", certainly does not make any sense in economics (according to your reasoning). It also follows from your logic that Joseph Doob's Optional Stopping Time "Theorem" is just merely another collection of equivalences which "says" one cannot devise a "strategy" to beat the market when the stock prices follows a martingale. Surely one needs to know what a stopping time is (in addition to filtration). 2.Watereddown mathematic suffice, since economists only uses it as a tool? In financial econometrics, how do one estimate Stochastic Volatility Models with Levy jumps without knowing what acutally an Ito Integral is, the "theories and theorems" behind stochastic "Differential" Equation (as opposed to "difference" equations frequently adopted in economics) and Levy Process with jumps, what about Levy without cadlag sample paths? how to derive the density for the first hitting time of Brownian motion? With only a comprehension of waterdowned level mathematics, one's research in economics would be confined to a subset of topics, areas like Stochastic Differential Games, Mathematical Finance would be out of one's league. And it is very hard to see how ideas come into play with a "watered down toolbox" to develop or even follow one's so called "idea". Mathematics is all about ideas, just that when one lost comprehension , one only sees a densed set of Greeks flying around.....hence your so called "formalization".
  2. This is so true! just an example...the probablity theories and stochastic processes are often watered down in economics....i.e. This notation Et[Xt+1] - conditional expectation is always used in macroeconomics .....its actually a function rather than an expected value but it is seldom addressed appropriately...........the martingales in many macroeconomic textbook (say Sargent) are another examples of martinagles "without" filtrations!
  3. NYU sent out fellowship offers..so what is the situation of non funded and waitlist, anyone got waiting for these?
  4. has anyone checked out mercedes...?
  5. someone posted a reject on gradcafe...so NW is firing again
  6. Hi Guys. For Columbia, I am surprised that they admitt 52 ppl, seems like in the past 2 yrs Columbia has only less than 10 first year?? For NYU, Did they emailed the large waitlist ppl? Should I assume I am out? I emailed the grad coordinator...no reply again, Who is the admission chair?
  7. useful if u mean who's not among the econ faculty at NWU
  8. Does anyone know who's in the adcom this year for Northwestern, Chicago and Penn?
  9. anyone contacted Mercedes?
  10. What is rolling admission?What exactly did Kelly says?
  11. I am out for Columbia as well....just waiting for NYU, Carnegie Mellon. Anyone waiting for NYU?
  12. did u apply to NYU and Carnegie Mellon? Which schools exactly are you waiting for?
  13. hey u guys math major in the States?
  14. hey guys...anyone applying to NYU PhD MAth? I heard its pretty easy to get in but very hard to get funded
  15. anyone who is still waiting results for the captioned? To "Penn MAth", where else did u apply?
  16. so most of the funded offers from Penn gone? does anyone (those who's not from "the boot") know what Kelly says? (i.e. the typical - no decision has yet been made or....?)
  17. its a no brainer. you really wanna try again??? getting a math/stat BA? Do you (((understand))) "opportunity cost"? (in terms 4 years salary from any decent job...couldnt be worser than from Mcdonald)
  18. books are too time consuming to read, but I believe lecture notes would be suffice. Here is one 14 pages that I believe would be suffice, http://www.math.binghamton.edu/paul/505-S07/LectureNotes4.pdf. Cantor set is measure zero Fat cantor set has positive measure hence contains a non measurable set M map (homeo) M into C, it follows f(M) is not borel measurable but is a subset in C (null set) hence f(M) is in L1. But it is not in B1 (f(M) is not borel measurable).
  19. One example are some subsets of Cantor set. In B1 and L1. for higher dimension it is even easier to prove such set that is in L but not in B....one such example is....pick a vitali set V pick N=Rx{0} (null set), then N is in both B1xB1=B2 and L2 i.e.completion of B1XB1 product space, it follows Vx{0} is a subset of Rx{0} hence must be in L2 (completeness). Nevertheless Vx{0} is not in B1xB1=B2, for if it is, then the y cut of Vx{0} at y=0 would be V which surely not in L1 let alone B1.
  20. To understand the difference briefly, you need to know what is an outer measure and its construction and complete measure space, and why do we need such a construction, look it up in wiki for two things should be suffice "outer measure and completeness" Their difference lines in completeness, i.e. lebesgue contains a wider class of null sets. In Economics, Prob theory, working with Borel measure (Lebegue measure reduced to the Borel set) is suffice,since we dunt need a sigma algebra as big as Lebesgue.
  21. I edited it, I was wrong, positve / non negative fucntions 's image is in R+, I meant its domain, which is in D=[o,inf) so f is in Cn(D) as opposed to Cn®
  22. I guest this may be helpful, since the original problem doesnt define precisely this f:X-Y I guest the more precise problem should be that f:R+-R where f is in Cn(R+) the vector space of nth continuously differentiable funtions defined on [0,inf). f prime is still continuous at x=0. (one side continuity suffice since f is not defined for x
  23. My misunderstanding, my fault, my apologise.
×
×
  • Create New...