scholarly journals Affine processes on positive semidefinite matrices

2011 ◽  
Vol 21 (2) ◽  
pp. 397-463 ◽  
Author(s):  
Christa Cuchiero ◽  
Damir Filipović ◽  
Eberhard Mayerhofer ◽  
Josef Teichmann
Keyword(s):  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Affine Processes

scholarly journals Affine Processes on Positive Semidefinite Matrices

2009 ◽  
Author(s):  
Christa Cuchiero ◽  
Damir Filipovic ◽  
Eberhard Mayerhofer ◽  
Josef Teichmann
Keyword(s):  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Affine Processes

scholarly journals Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

2020 ◽  
Vol 52 (3) ◽  
pp. 825-854
Author(s):  
Martin Friesen ◽  
Peng Jin ◽  
Jonas Kremer ◽  
Barbara Rüdiger
Keyword(s):  
Limit Distribution ◽  
Positive Semidefinite ◽  
Wasserstein Distance ◽  
The State ◽  
Time Behavior ◽  
Positive Semidefinite Matrices ◽  
Affine Processes ◽  
The Laplace Transform ◽  
Long Time ◽  
First Moment

AbstractThis article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite $d\times d$ matrices. In particular, for conservative and subcritical affine processes we show that a finite $\log$ -moment of the state-independent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: first, in a specific metric induced by the Laplace transform, and second, in the Wasserstein distance under a first moment assumption imposed on the state-independent jump measure and an additional condition on the diffusion parameter.

scholarly journals A trace bound for integer-diagonal positive semidefinite matrices

2020 ◽  
Vol 8 (1) ◽  
pp. 14-16
Author(s):  
Lon Mitchell
Keyword(s):  
Positive Semidefinite ◽  
Positive Semidefinite Matrix ◽  
Positive Semidefinite Matrices ◽  
Semidefinite Matrix

AbstractWe prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.

scholarly journals Fischer Type Log-Majorization of Singular Values on Partitioned Positive Semidefinite Matrices

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Benju Wang ◽  
Yun Zhang
Keyword(s):  
Singular Values ◽  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Fischer’S Inequality ◽  
New Inequalities

In this paper, we establish a Fischer type log-majorization of singular values on partitioned positive semidefinite matrices, which generalizes the classical Fischer's inequality. Meanwhile, some related and new inequalities are also obtained.

scholarly journals A Characterization of Polynomial Density on Curves via Matrix Algebra

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1231
Author(s):  
Carmen Escribano ◽  
Raquel Gonzalo ◽  
Emilio Torrano
Keyword(s):  
Matrix Algebra ◽  
Optimization Problems ◽  
Positive Semidefinite ◽  
Point Of View ◽  
Alternative Proof ◽  
General Context ◽  
Positive Semidefinite Matrices ◽  
Jordan Curves ◽  
Point Evaluations

In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces L 2 ( μ ) , with μ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix with the measure μ . To do it, in the more general context of Hermitian positive semidefinite matrices, we introduce two indexes, γ ( M ) and λ ( M ) , associated with different optimization problems concerning theses matrices. Our main result is a characterization of density of polynomials in the case of measures supported on Jordan curves with non-empty interior using the index γ and other specific index related to it. Moreover, we provide a new point of view of bounded point evaluations associated with a measure in terms of the index γ that will allow us to give an alternative proof of Thomson’s theorem, by using these matrix indexes. We point out that our techniques are based in matrix algebra tools in the framework of Hermitian positive definite matrices and in the computation of certain indexes related to some optimization problems for infinite matrices.

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