References of "Jaramillo Gil, Arturo 50032018"
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See detailApproximation of Fractional Local Times: Zero Energy and Derivatives
Jaramillo Gil, Arturo UL; Nourdin, Ivan UL; Peccati, Giovanni UL

in Annals of Applied Probability (2021), In press

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See detailFluctuations for matrix-valued Gaussian processes
Jaramillo Gil, Arturo UL; Pardo Millan, Juan Carlos; Diaz Torres, Mario Alberto

E-print/Working paper (2020)

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 ... [more ▼]

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. [less ▲]

Detailed reference viewed: 57 (4 UL)