bio | website | users.wpi.edu/~ssturm |
---|---|---|
location | Worcester, MA | |
age | 36 | |
visits | member for | 2 years, 4 months |
seen | 3 hours ago | |
stats | profile views | 340 |
Assistant Professor at Worcester Polytechnic Institute
Research interests: Mathematical Finance, Stochastic Analysis
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 |
Jun 26 |
reviewed | No Action Needed Suggestions for a good Measure Theory book |
Apr 4 |
comment |
Rapid evaluation of multivariate normal integral
@an12 If you use Monte-Carlo techniques, you may use symmetry for variance reduction via antithetic sampling. |
Apr 4 |
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Rapid evaluation of multivariate normal integral
Why calculating the integral and not just trying an acceptance-rejection type approach? - Simulating the $(n+1)$st variable and comparing it with other $n$ normal pdfs? This should be faster then integration. If you want hard bounds, you could try to some Quasi-Monte Carlo based sampling. [But this is maybe a bit trickier, as you have to keep the low discrepancy while transforming uniform distributions in normal ones...] |
Apr 3 |
comment |
Reference needed: Donsker's Invariance Principle for Riemannian Manifolds
Great lecture notes on Donsker's theorem in $\mathbb{R}$. However, I do not see how this could be applied to a generic manifold setting. |
Mar 13 |
answered | Good books on stochastic partial differential equations? |
Mar 7 |
awarded | Yearling |