In this paper we study upper bounds for the density of solution of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H > 1/2, the density of the solution satisfy the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough c...

In this paper we study upper bounds for the density of solution to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H > 1/2, the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough...

ABSTRACT. We study those smooth complex hypersurfaces W in C having the property that all holomorphic functions of finite weighted L norm on W extend to entire functions with finite weighted L norm. Such hypersurfaces are called interpolation hypersurfaces. We also examine the dual problem of finding all sampling hypersurfaces, i.e., smooth hypersurfaces W in C such that any entire function wit...

In the first ‘Wavelets and Statistics’ conference proceedings 1, our group published ‘Wavelab and Reproducible Research’, in which we advocated using the internet for publication of software and data so that research results could be duplicated by others. Much has happened in the last decade that bears on the notion of reproducibility, and we will review our experience. We will also describe a ...

We provide a unifying geometric framework for the analysis of general classes of duality schemes and penalty methods for nonconvex constrained optimization problems. We present a separation result for nonconvex sets via general concave surfaces. We use this separation result to provide necessary and sufficient conditions for establishing strong duality between geometric primal and dual problems...

In this paper, geometric interpolation by parametric polynomial curves is considered. Discussion is focused on the case where the number of interpolated points is equal to r + 2, and n = r denotes the degree of the interpolating polynomial curve. The interpolation takes place in Rd with d = n. Even though the problem is nonlinear, simple necessary and sufficient conditions for existence of the ...

We consider a convex polygonal heat conductor whose inscribed circle touches every side of the conductor. Initially, the conductor has constant temperature and, at every time, the temperature of its boundary is kept at zero. The hot spot is the point at which temperature attains its maximum at each given time. It is proved that, if the hot spot is stationary, then the conductor must satisfy two...

A conditional geometric phase shift gate, which is fault tolerant to certain types of errors due to its geometric nature, was realized recently via nuclear magnetic resonance(NMR) under adiabatic conditions. By the adiabatic requirement, the result is inexact unless the Hamiltonian changes extremely slowly. However, in quantum computation, everything must be completed within the decoherence tim...

Abstract. We consider the problem of variable selection in highdimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in Hilbert spaces and consists of comparing the norms of the projections of the data onto various additive subspaces. Under minimal geometric assumpti...

Intrinsic dynamics of the central vestibular system (CVS) appear to be at least partly determined by the symmetries of its connections. The CVS contributes to whole-body functions such as upright balance and maintenance of gaze direction. These functions coordinate disparate senses (visual, inertial, somatosensory, auditory) and body movements (leg, trunk, head/neck, eye). They are also unified...