Xinghua Zheng
On the Estimation of Integrated Covariance Matrices of High Dimensional Diffusion Processes.
Wed, 05/12/2010 - 15:01 — SomNambulAuthors: Xinghua Zheng, Yingying Li
Subjects: Methodology
AbstractWe consider the estimation of integrated covariance matrices of high
dimensional diffusion processes by using high frequency data. We start by
studying the most commonly used estimator, the realized covariance matrix
(RCV). We show that in the high dimensional case when the dimension p and the
observation frequency n grow in the same rate, the limiting empirical spectral
distribution of RCV depends on the covolatility processes not only through the
underlying integrated covariance matrix Sigma, but also on how the covolatility
processes vary in time.Critical Branching Random Walks with Small Drift.
Fri, 11/13/2009 - 16:01 — SomNambulAuthors: Xinghua Zheng
Subjects: Probability
AbstractWe study critical branching random walks (BRWs) $U^{(n)}$ on $\zz{Z}_{+}$
where for each $n$, the displacement of an offspring from its parent has drift
$2\beta/\sqrt{n}$ towards the origin and reflection at the origin. We prove
that conditional on survival to generation $n^{\alpha}$, the maximal
displacement is $O_p(\sqrt{n^\alpha})$ if $\alpha \leq 1$ and is asymptotically
equivalent to $(\alpha-1)/(4\beta)\cdot \sqrt{n}\log n$ if $\alpha>1$.The random conductance model with Cauchy tails.
Fri, 08/21/2009 - 19:51 — SomNambulAuthors: Martin T. Barlow, Xinghua Zheng
Subjects: Probability
AbstractWe consider a random walk in an i.i.d. Cauchy-tailed conductances
environment. We obtain a quenched functional CLT for the suitably rescaled
random walk, and, as a key step in the arguments, we improve the local limit
theorem for $p^\om_{n^2 t}(0,y)$ in [BD09, Theorem 5.14] to a result which
gives uniform convergence for $p^\om_{n^2 t}(x,y)$ for all $x, y$ in a ball.
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