393 reputation
1310
bio website users.wpi.edu/~ssturm
location Worcester, MA
age 36
visits member for 2 years, 9 months
seen 9 hours ago
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
comment 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
comment 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
comment 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
comment 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
comment explicit characterization of the stochastic integrand
Related question: mathoverflow.net/questions/106808/…
Feb
27
comment right-continuity of filtration
While not an exact duplicate, does this answer your question? mathoverflow.net/questions/46957/…
Feb
22
comment 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
comment 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
comment 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
comment 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
comment 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
comment 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