bio | website | users.wpi.edu/~ssturm |
---|---|---|
location | Worcester, MA | |
age | 36 | |
visits | member for | 2 years, 7 months |
seen | 32 mins ago | |
stats | profile views | 351 |
Assistant Professor at Worcester Polytechnic Institute
Research interests: Mathematical Finance, Stochastic Analysis
Jul 20 |
comment |
Progressively measurable vs adapted
I think this is most easily seen by considering a counterexample. Let $(X(t))_{t\geq 0}$ be a deterministic, non-Borel-masurable function. Then this is clearly a stochastic process that is not progressively measurable. However, as for every $t$, $X(t)$ is just a constant, the process is trivially adapted to any filtration you want (as constants are measureable w.r.t. the trivial sigma field). |
Jul 19 |
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Rediscovery of lost mathematics
A good overview of Doblin's work in the "pli chachete" is given in this article by Bernard Bru and Marc Yor: ams.org/mathscinet/search/… |
Jul 19 |
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Rediscovery of lost mathematics
I am not sure how much this can count as rediscovery. There is no stochastic integral in Doblin's paper, and hence no actual Ito formula. What Doblin does, is to give a probabilistic characterization of a diffusion in terms of a time-changed Brownian motion. On the other hand this can be considered as even more anticipating, as the connection of random time changes and stochastic integrals was only discovered in 1965, by Dubins-Schwarz and Dambis... |
Apr 30 |
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Applied Math author order
@IgorRivin: SSRN has annoying feature to list first the submitting author, if you take not great precaution to avoid it. And after fact it is hard to change this. Thus the ordering in the html mask of SSRN differs often from the ordering in the actual paper. One should check really pdf. E.g, the first paper following your link is given as Goetzmann, Ibbotson and Brown, however if you do the actual work and load down the pdf, you will see that the actual order is Brown, Goetzmann and Ibbotson. |
Apr 30 |
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Applied Math author order
Applied Math is a huge field and conventions might be influenced by the field in which the applications lie. E.g., in financial math, alphabetical order is the standard (I would guess >98% of all papers). |
Apr 29 |
awarded | Nice Answer |
Apr 3 |
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explicit characterization of the stochastic integrand
Related question: mathoverflow.net/questions/106808/… |
Feb 27 |
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right-continuity of filtration
While not an exact duplicate, does this answer your question? mathoverflow.net/questions/46957/… |
Feb 22 |
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The regularity of Levy process
I do not know where in the paper you found the statement "hit with probability one". I can only find "hit with positive probability". |
Jan 14 |
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why is it so cool to square numbers? (in terms of finding the standard deviation)
@isomorphismes It has more random variables with finite norm. And it implies that two random variables with finite variance have also a finite covariance. |
Oct 16 |
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Random vs Unknown
Just to complement Steven's excellent answer. The example he gives is commonly known as Ellsberg paradox (yes, the Pentagon papers Ellsberg). His original articles makes still a very pleasant read: Risk, Ambiguity, and the Savage Axioms: rand.org/content/dam/rand/pubs/papers/2008/P2173.pdf One way to deal with uncertainty mathematically are robust preferences. For a nice and thorough introduction see, e.g., chapter 2 of Foellmer and Schied. Stochastic Finance. An introduction in discrete time. |
Oct 8 |
awarded | Constituent |
Oct 6 |
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Maximum of a sequence of $n$ positive random variables where variance is an increasing function of $n$
So in fact you want a statement about the sequence of maxima $X_{\max}^n = \max\{ X_1^n, \ldots, X_n^n\}$ where $X_1^n, \ldots, X_n^n$ are iid with variance $\sigma(n)$? |
Oct 4 |
revised |
Distribution of last time Brownian motion crosses a line
deleted 32 characters in body |
Oct 4 |
answered | Distribution of last time Brownian motion crosses a line |
Oct 1 |
awarded | Caucus |
Aug 26 |
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Upper bound on the maxima of ratio of expectation of quantities under Gaussian measure
It looks like this is connected to the Esscher transform (see en.wikipedia.org/wiki/Esscher_transform and en.wikipedia.org/wiki/Esscher_principle). |
Jun 29 |
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When is a coarsening of a Markov chain Markov?
A general criterion when the function of a Markov chain is again a Markov chain is given in the following article: F. P. Kelly, Markovian Functions of a Markov Chain, Sankhyā: The Indian Journal of Statistics, Series A (1961-2002) , Vol. 44, No. 3 (Oct., 1982), pp. 372-379. Link: jstor.org/stable/25050326 |
Jun 26 |
reviewed | No Action Needed Suggestions for a good Measure Theory book |
Jun 26 |
awarded | Custodian |