Matrizentheorie

Gantmacher, Felix R.

doi:10.1007/978-3-642-71243-2

Cited by 166 publications

(133 citation statements)

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“…Recall from [10] that a matrix A ∈ M n (C) is called indecomposable if the set I = {1, 2, · · · , n} cannot be written as a disjoint union I = J 1 ∪ J 2 with J 1 = ∅ and J 2 = ∅, in such a way that a uv = 0 whenever u ∈ J 1 and v ∈ J 2 . Proof.…”

Section: Observe That We Have X ∼ Y If and Only Ifmentioning

confidence: 99%

On Normal Tensor Functors and Coset Decompositions for Fusion Categories

Bruguières¹,

Burciu²

2014

Appl Categor Struct

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Abstract. We introduce the notion of double cosets relative to two fusion subcategories of a fusion category. Given a tensor functor F : C → D between fusion categories, we introduce an equivalence relation ≈ F on the set Λ C of isomorphism classes of simple objects of C, and when F is dominant, an equivalence relation ≈ F on Λ D . We show that the equivalent classes of ≈ F are cosets. We also give a description of the image of F when it is a normal tensor functor, and we show that F is normal if and only if the images of ≈ F equivalent elements of Λ C are colinear. We study the situation where the composition of two tensor functors F = F ′ F ′′ is normal, and we give a criterion of normality for F ′′ , with an application to equivariantizations. Lastly, we introduce the radical of a fusion subcategory and compare it to its commutator in the case of a normal subcategory. We also give a description for the image of a normal tensor functor between any two fusion categories.

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Section: Observe That We Have X ∼ Y If and Only Ifmentioning

confidence: 99%

On Normal Tensor Functors and Coset Decompositions for Fusion Categories

Bruguières¹,

Burciu²

2014

Appl Categor Struct

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“…Let L(θ, X T ) denote the likelihood function of observations X T = {X t , 0 ≤ t ≤ T } of the process introduced in (1) provided with the mean reversion function (2). If the drift term given in (3) satisfies condition (5) then…”

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

“…We make use of the following formula for the inverse of a partitioned matrix which can be deduced from the Frobenius matrix inversion formula, cf. Gantmacher [2], p. 73. Alternatively the formula can also be verified directly.…”

Section: Maximum Likelihood Estimation For a Periodic Mean Reversion mentioning

confidence: 99%

Drift estimation for a periodic mean reversion process

Dehling

Franke

Kott

2010

Stat Inference Stoch Process

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Abstract. In this paper we propose a periodic, mean-reverting Ornstein-Uhlenbeck process of the form dX t = (L(t) − α X t ) dt + σ dB t , t ≥ 0, where L(t) is a periodic, parametric function. We apply maximum likelihood estimation for the drift parameters based on time-continuous observations. The estimator is given explicitly and we prove strong consistency and asymptotic normality as the observed number of periods tends to infinity. The essential idea of the asymptotic study is the interpretation of the stochastic process as a sequence of random variables that take values in some function space.

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“…By the Perron theorem (see [Gan88]), the positive matrix b q ij possesses a positive eigenvector (e 0 (q), . .…”

Section: §5 Markov Measuresmentioning

confidence: 99%

Statistical estimation of measure invariants

Timofeev

2006

St. Petersburg Math. J.

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Abstract. New invariants of measures, called the β-statentropy, are described. They are similar to the entropy and the HP -spectrum for dimensions. The β-statentropy admits construction of a statistical estimator calculated by n independent points distributed in accordance with a given measure. The accuracy of this estimator is O(n −c ), where c is some constant, and the complexity of calculation is O(n 2 ).It is shown that for an exact dimensional measure the 0-statentropy coincides with the Hausdorff dimension, and for a Markov measure the β-statentropy coincides with the HP -spectrum for dimensions.An application of the β-statentropy to finding the entropy and dimensional characteristics of dynamical systems is described.

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Matrizentheorie

Cited by 166 publications

References 0 publications

On Normal Tensor Functors and Coset Decompositions for Fusion Categories

On Normal Tensor Functors and Coset Decompositions for Fusion Categories

Drift estimation for a periodic mean reversion process

Statistical estimation of measure invariants

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