2,292 reputation
622
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location Rehovot, Israel
age 24
visits member for 3 years, 3 months
seen 11 hours ago

I'm a PhD student in Weizmann Institute, specializing in Probability.


Jun
15
comment Generalization of Krull dimension for commutative rings
Cardinals can be constructed as a sub-class of ordinals, so they are well-ordered.
Jun
14
comment Generalization of Krull dimension for commutative rings
In any case, there is always a smallest cardinality $\alpha$, such that there are no chains of length $\ge \alpha$, which can serve as an alternative notion of dimension.
Jun
14
revised Generalization of Krull dimension for commutative rings
added 115 characters in body
Jun
14
answered Generalization of Krull dimension for commutative rings
Jun
12
comment $BMO$-property via a John-Nirenberg type estimate?
I meant any of the equivalent norms in the Orlicz space with a function that grows exponentially - e.g. $\Phi(x) := \cosh x - 1$. For the definition of Orlicz space see en.wikipedia.org/wiki/Birnbaum%E2%80%93Orlicz_space.
Jun
11
revised $BMO$-property via a John-Nirenberg type estimate?
added 10 characters in body
Jun
11
revised $BMO$-property via a John-Nirenberg type estimate?
added 10 characters in body
Jun
11
answered $BMO$-property via a John-Nirenberg type estimate?
Jun
4
awarded  Nice Answer
Jun
4
answered which norms can be realized as operator norms?
Jun
1
awarded  Revival
Apr
24
comment Quadratic variation and predictable quadratic variation for martingales
On second thought, since you define $\langle M \rangle$ in such a way that it doesn't always exist, it's not even clear what your statement means...
Apr
24
comment Quadratic variation and predictable quadratic variation for martingales
Besides, for continuous martingales $[M]$ and the properly defined $\langle M \rangle$ (i.e. $M^2 - \langle M \rangle$ is a local martingale) are equal.
Apr
24
comment Quadratic variation and predictable quadratic variation for martingales
There is absolutely no reason for $\mathsf{E} \left[ (M_t - M_s)^2 \, \middle| \, \mathcal{F}_s \right]$ to be almost surely finite, so your statement is certainly not true without additional integrability assumptions. That being said, I believe your statement is indeed true for martingales that are bounded in the $L^2$ norm.
Apr
8
awarded  Yearling
Mar
20
asked Is Wiener's Tauberian theorem true in Wiener space?
Feb
25
answered Location of maximum of Brownian motion with rough drift
Feb
16
comment Location of maximum of Brownian motion with rough drift
I'll try to cook up a readable answer later...
Feb
16
comment Location of maximum of Brownian motion with rough drift
... which is not in the $W^{1,2}$ Sobolev space, so $\intop f d \mathsf{E} U$ doesn't converge for some $f \in L^2$. So the distributions of $B$ and $(B + U) / \sqrt 2$ must be singular to each other: one needs the recentering and the other one doesn't.
Feb
16
comment Location of maximum of Brownian motion with rough drift
... And this can be done using various invariants of the equivalence class of the distribution of Bessel(3). For instance, the stochastic integrals $\intop f(t) d (U_t - \mathsf{E} U_t)$ converge for all deterministic $f \in L^2$, so also the stochastic integrals $\intop f(t) d ((B_t + U_t) / \sqrt 2 - \mathsf{E} U_t / \sqrt 2)$ converge for such $f$. For the Brownian motion (and any other semimartingale with distribution equivalent to that of a Brownian motion) such integrals would converge without the $\mathsf{E} U_t$ recentering. Note that $\mathsf{E} U_t = \mathsf{const} \cdot t^{1/2}$...