383 reputation
139
bio website users.wpi.edu/~ssturm
location Worcester, MA
age 36
visits member for 2 years, 4 months
seen 3 hours ago
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
comment 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