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Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schr¨odinger equation with septic and higher power-law nonlinearities and an external potenti...
Most business processes are, by nature, multivariate and autocorrelated. Highdimensionality is rooted in processes where more than one variable is considered simultaneously to provide a more comprehen...
We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourie...
We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the select...
We consider dimension reduction for regression or classification in which the predictors are matrix- or array-valued. This type of pre- dictor arises when measurements are obtained for each combinat...
Mouvements browniens asymetriques modifies en dimension finie et operateurs differentiels a coefficients discontinus。
Labyrinth dimension of Brownian trace      Labyrinth dimension  Brownian trace        font style='font-size:12px;'> 2009/9/22
Suppose that X is a two-dimensional Brownian motion. The trace X[O, I] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.
Let X(t) (ts R,) be an u-self-similar Markov process on Rd or Rd+. The Hausdorff dimension of the image, graph and zero set of X(t) are obtained under certain mild conditions. Similar results are a...
We prove that under a general condition interpolation dimensions of H-sssi process converge in probabiIity to 2-H. The result can be applied to a wide class of H-sssi processes which includes fract...
Let $B$ be a two dimensional Brownian motion and let the frontier of $B[0,1]$ be defined as the set of all points in $B[0,1]$ that are in the closure of the unbounded connected component of its comple...
Percolation Dimension of Brownian Motion in R^3     Brownian Motion  Percolation Dimension       font style='font-size:12px;'> 2009/5/8
Let $B(t)$ be a Brownian motion in $R^3$. A {it subpath} of the Brownian path $B[0,1]$ is a continuous curve $gamma(t)$, where $gamma[0,1] subseteq B[0,1]$ , $gamma(0) = B(0)$, and $gamma(1) = B(1)$. ...
Support of a Marcus equation in Dimension 1     Marcus equation  pathwise representation  support theorem       font style='font-size:12px;'> 2009/5/4
The purpose of this note is to give a support theorem in the Skorohod space for a one-dimensional Marcus differential equation driven by a Lévy process, without any assumption on the latter. We also g...
A short proof of the Hausdorff dimension formula for Levy processes      Levy processes  Hausdor dimension  range       font style='font-size:12px;'> 2009/4/22
A different but very short proof of a recent result of Khoshnevisan.
In Chen and Li (2004), large deviations were obtained for the spatial $L^p$ norms of products of independent Brownian local times and local times of random walks with finite second moment. The methods...
We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension d≥2

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