On the Process of the Eigenvalues of a Hermitian Lévy process

Autor:	Alfonso Rocha-Arteaga, Victor Pérez-Abreu
Rok vydání:	2015
Předmět:	Pure mathematics Stochastic differential equation Rank (linear algebra) Mathematical analysis Jump Commutative property Hermitian matrix Lévy process Noncommutative geometry Eigenvalues and eigenvectors Mathematics
Zdroj:	The Fascination of Probability, Statistics and their Applications ISBN: 9783319258249
DOI:	10.1007/978-3-319-25826-3_11
Popis:	The dynamics of the eigenvalues (semimartingales) of a Levy process X with values in Hermitian matrices is described in terms of Ito 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::28f73f5e040872edbd801c1c4305f505 https://doi.org/10.1007/978-3-319-25826-3_11 Zobrazit plný text záznamu