Reference : Fluctuations for matrix-valued Gaussian processes
 Document type : E-prints/Working papers : Already available on another site Discipline(s) : Engineering, computing & technology : Multidisciplinary, general & others To cite this reference: http://hdl.handle.net/10993/44712
 Title : Fluctuations for matrix-valued Gaussian processes Language : English Author, co-author : Jaramillo Gil, Arturo [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >] Pardo Millan, Juan Carlos [] Diaz Torres, Mario Alberto [] Publication date : 11-Jan-2020 Peer reviewed : No Keywords : [en] Malliavin calculus ; alued Gaussian processes ; central limit theorem Abstract : [en] We consider a symmetric matrix-valued Gaussian process $Y^{(n)}=(Y^{(n)}(t);t\ge0)$ and its empirical spectral measure process $\mu^{(n)}=(\mu_{t}^{(n)};t\ge0)$. Under some mild conditions on the covariance function of $Y^{(n)}$, we find an explicit expression for the limit distribution of $$Z_F^{(n)} := \left( \big(Z_{f_1}^{(n)}(t),\ldots,Z_{f_r}^{(n)}(t)\big) ; t\ge0\right),$$ where $F=(f_1,\dots, f_r)$, for $r\ge 1$, with each component belonging to a large class of test functions, and $$Z_{f}^{(n)}(t) := n\int_{\R}f(x)\mu_{t}^{(n)}(\ud x)-n\E\left[\int_{\R}f(x)\mu_{t}^{(n)}(\ud x)\right].$$ More precisely, we establish the stable convergence of $Z_F^{(n)}$ and determine its limiting distribution. An upper bound for the total variation distance of the law of $Z_{f}^{(n)}(t)$ to its limiting distribution, for a test function $f$ and $t\geq0$ fixed, is also given. Funders : University of Luxembourg Name of the research project : R-AGR-3410-12-Z (MISSILe) Target : Researchers ; Professionals Permalink : http://hdl.handle.net/10993/44712 Other URL : https://arxiv.org/pdf/2001.03718.pdf FnR project : FnR ; FNR13242276 > Arturo Jaramillo Gil > > Malliavin calculus and Stein’s method at Singapore and Luxembourg > 01/09/2018 > 31/08/2020 > 2017

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