Reference : Fluctuations for matrix-valued Gaussian processes |
E-prints/Working papers : Already available on another site | |||
Engineering, computing & technology : Multidisciplinary, general & others | |||
http://hdl.handle.net/10993/44712 | |||
Fluctuations for matrix-valued Gaussian processes | |
English | |
Jaramillo Gil, Arturo ![]() | |
Pardo Millan, Juan Carlos [] | |
Diaz Torres, Mario Alberto [] | |
11-Jan-2020 | |
No | |
[en] Malliavin calculus ; alued Gaussian processes ; central limit theorem | |
[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. | |
University of Luxembourg | |
R-AGR-3410-12-Z (MISSILe) | |
Researchers ; Professionals | |
http://hdl.handle.net/10993/44712 | |
https://arxiv.org/pdf/2001.03718.pdf | |
FnR ; FNR13242276 > Arturo Jaramillo Gil > > Malliavin calculus and Stein’s method at Singapore and Luxembourg > 01/09/2018 > 31/08/2020 > 2017 |
File(s) associated to this reference | ||||||||||||||
Fulltext file(s):
| ||||||||||||||
All documents in ORBilu are protected by a user license.