On Filtering of Stochastic Volatility

Aihara, Shin Ichi

doi:10.9746/sicetr1965.37.727

Cited by 5 publications

(15 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was conjectured by Schreyer [ (2)]. The next result guarantees the validity of Schreyer's conjecture in the case where R is a Henselian local ring whose completion R is an isolated singularity.…”

Section: Extension-closed Subcategories and Annihilation Of Cohomologysupporting

confidence: 67%

“…Christensen, Krause and Kussin [14,25] showed that rings of finite global dimension have finite derived dimension, see also [30,Proposition 8.3]. More recently, Aihara and Takahashi [2] proved that derived dimension of a complete local ring with perfect coefficient field is finite. For small values of derived dimension, a number of definitive results have been obtained.…”

Section: Definition 22mentioning

confidence: 99%

See 1 more Smart Citation

Annihilation of Cohomology, Generation of Modules and Finiteness of Derived Dimension

et al. 2016

View full text Add to dashboard Cite

Abstract. Let (R, m, k) be a commutative noetherian local ring of Krull dimension d. We prove that the cohomology annihilator ca(R) of R is m-primary if and only if for some n ≥ 0 the n-th syzygies in mod R are constructed from syzygies of k by taking direct sums/summands and a fixed number of extensions. These conditions yield that R is an isolated singularity such that the bounded derived category D b (R) and the singularity category D sg (R) have finite dimension, and the converse holds when R is Gorenstein. We also show that the modules locally free on the punctured spectrum are constructed from syzygies of finite length modules by taking direct sums/summands and d extensions. This result is exploited to investigate several ascent and descent problems between R and its completion R.

show abstract

Section: Extension-closed Subcategories and Annihilation Of Cohomologysupporting

confidence: 67%

Section: Definition 22mentioning

confidence: 99%

Annihilation of Cohomology, Generation of Modules and Finiteness of Derived Dimension

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Definition-Theorem 3.2. [AI,Ai1] Let T and U be tilting complexes of Λ. We write T ≥ U if Hom K b (proj Λ) (T, U [n]) = 0 for any positive integer n. Then ≥ induces a partial order structure on tilt Λ.…”

Section: Homological and Algebraic Preliminariesmentioning

confidence: 99%

“…Preliminaries. We first recall some results about tilting mutation theory from [AI,Ai1,AIR]. Throughout this subsection, Λ is assumed to be a finite dimensional symmetric algebra.…”

Section: Condition Which Failsmentioning

confidence: 99%

See 1 more Smart Citation

Classification of two-term tilting complexes over Brauer graph algebras

2017

View full text Add to dashboard Cite

show abstract

Dimensions of triangulated categories with respect to subcategories

et al. 2014

View full text Add to dashboard Cite

This paper introduces a concept of dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upper bounds of the dimension with respect to a contravariantly finite subcategory and a resolving subcategory are given. Our methods not only recover some known results on the dimensions of derived categories in the sense of Rouquier, but also apply to various commutative and non-commutative noetherian rings.

show abstract

On Filtering of Stochastic Volatility

Cited by 5 publications

References 5 publications

Annihilation of Cohomology, Generation of Modules and Finiteness of Derived Dimension

Annihilation of Cohomology, Generation of Modules and Finiteness of Derived Dimension

Classification of two-term tilting complexes over Brauer graph algebras

Dimensions of triangulated categories with respect to subcategories

Contact Info

Product

Resources

About