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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 $(\mathcal{F}_t)_{... 1answer 2k views ### Right-continuity of natural filtrations My question: Is the natural filtration of a right-continuous process also right-continuous? I would say yes, but don't know where to start proving it. Thanks for your help/ideas! 2answers 418 views ### Does there exist a functorial splitting for the weight filtration (of singular cohomology)? There are plenty of examples of varieties whose singular cohomology with rational coefficients considered as a mixed Hodge structure does not decompose as the direct sum of its pure (weight) factors. ... 1answer 707 views ### Do Deligne's decalage and two filtrations for mixed Hodge complexes have a conceptual explanation? As far as I understood, there are two way to assign weights to a mixed Hodge complex (a way that does not depend on shifts, and another one that does). There is a clever way to relate these to ways ... 2answers 280 views ### Is the first filtration Hausdorff? Maybe this is too technical and elementary, but I cannot make up my mind, nor find a reference. The situation is the following: let$X$be a double cochain (right half-plane) complex of abelian ... 1answer 543 views ### Semistable filtered vector spaces, a Tannakian category. Let$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 \...
Given a filtered vector space (or module over a ring) $0=V_{0}\subseteq V_{1}\subseteq\cdots\subseteq V$, you can construct the associated graded vector space \$\mathrm{gr}\left(V\right)=\oplus_{i}V_{i+...