On the Process of the Eigenvalues of a Hermitian Lévy process View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2016

AUTHORS

Victor Pérez-Abreu , Alfonso Rocha-Arteaga

ABSTRACT

The dynamics of the eigenvalues (semimartingales) of a Lévy process X with values in Hermitian matrices is described in terms of Itô stochastic differential equations with jumps. This generalizes the well known Dyson-Brownian motion. The simultaneity of the jumps of the eigenvalues of X is also studied. If X has a jump at time t two different situations are considered, depending on the commutativity of X(t) and \(X(t-)\). In the commutative case all the eigenvalues jump at time t only when the jump of X is of full rank. In the noncommutative case, X jumps at time t if and only if all the eigenvalues jump at that time when the jump of X is of rank one. More... »

PAGES

231-249

References to SciGraph publications

  • 2011-03. Random matrices: Universality of local eigenvalue statistics in ACTA MATHEMATICA
  • 1990. Stochastic Integration and Differential Equations, A New Approach in NONE
  • 1997. Matrix Analysis in NONE
  • 1991-10. Wishart processes in JOURNAL OF THEORETICAL PROBABILITY
  • 2012-06. Random matrix models of stochastic integral type for free infinitely divisible distributions in PERIODICA MATHEMATICA HUNGARICA
  • 2006. Classical and Free Infinite Divisibility and Lévy Processes in QUANTUM INDEPENDENT INCREMENT PROCESSES II
  • 1992-06. The Wigner semi-circle law and eigenvalues of matrix-valued diffusions in PROBABILITY THEORY AND RELATED FIELDS
  • Book

    TITLE

    The Fascination of Probability, Statistics and their Applications

    ISBN

    978-3-319-25824-9
    978-3-319-25826-3

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-25826-3_11

    DOI

    http://dx.doi.org/10.1007/978-3-319-25826-3_11

    DIMENSIONS

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