The filtrations tag has no wiki summary.

**3**

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**1**answer

130 views

### Does martingale convergence hold for arbitrary time?

Let $\{\mathcal B_i:i\in I\}$ be a family of $\sigma$-algebras (over the same set $\Omega$) which are totally ordered by inclusion, in the sense that for any $i,j\in I$ either $\mathcal ...

**7**

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**5**answers

508 views

### Properties preserved under passage to augmented filtration

Dear all,
generally speaking, my question is about which properties of a stochastic process are preserved when I skip from the original to the augmented filtration.
Recall that if ...

**0**

votes

**0**answers

251 views

### Left-continuous poisson process?

Hi,
Is a left-continuous compensated poisson process a martingale under its natural filtration?
And what about the right-continuous version of its filtration? (My guess is no)
Thanks,
Johannes

**2**

votes

**1**answer

948 views

### Right-continuity of natural filtrations

My question: Is the natural filtration of a right-continuous process also right-continuous?
I would say yes, but don't know where to start proving it.
Thanks for your help/ideas!

**6**

votes

**2**answers

381 views

### Does there exist a functorial splitting for the weight filtration (of singular cohomology)?

There are plenty of examples of varieties whose singular cohomology with rational coefficients considered as a mixed Hodge structure does not decompose as the direct sum of its pure (weight) factors. ...

**3**

votes

**1**answer

627 views

### Do Deligne's decalage and two filtrations for mixed Hodge complexes have a conceptual explanation?

As far as I understood, there are two way to assign weights to a mixed Hodge complex (a way that does not depend on shifts, and another one that does). There is a clever way to relate these to ways ...

**3**

votes

**2**answers

263 views

### Is the first filtration Hausdorff?

Maybe this is too technical and elementary, but I cannot make up my mind, nor find a reference.
The situation is the following: let $X$ be a double cochain (right half-plane) complex of abelian ...

**14**

votes

**1**answer

463 views

### Semistable filtered vector spaces, a Tannakian category.

Let $k$ be a field (char = 0, perhaps). Let $(V,F)$ be a pair, where $V$ is a finite-dimensional $k$-vector space, and $F$ is a filtration of $V$, indexed by rational numbers, satisfying:
$F^i V ...

**5**

votes

**2**answers

323 views

### If associated-graded of a filtered bialgebra is Hopf, does it follow that the original bialgebra was Hopf?

Warning: older texts use the word "Hopf algebra" for what's now commonly called "bialgebra", whereas now "Hopf" is an extra condition. So as to avoid any confusion, I'll give my definitions before ...

**12**

votes

**2**answers

850 views

### What is the universal property of associated graded?

Given a filtered vector space (or module over a ring) 0=V0⊆V1⊆...⊆V, you can construct the associated graded vector space gr(V)=⊕iVi+1/Vi. Does gr(V) satisfy a universal property? ...