Search

We study the asymptotic behavior, in the zero noise limit, of solu­tions to Schrodinger's functional equations and that of h-pass pro­cesses, and give a new proof of the existence of the minimizer of Monge's problem with a quadratic cost.

We construct a random crystalline ( or polyhedral) approximation of a convexified Gauss curvature flow of bounded open sets in an anisotropic external field. We also show that a weak solution to the PDE which describes the motion of a bounded open set is unique and is a viscosity solution of it.

We shmv the existence of ,veak solutions to the PDE which de­scribes the motion by R-curvaturc in Rd , by the continuum limit of a class of infinite particle systems. We also show that weak solutions of the PDE arc viscosity solutions and give the uniqueness result on both weak and viscosity solutions.

We introduce covariance kernels for Borel probability measures on Rd, and study the relation between the central limit theorem in the total variation distance and the convergence of covariance kernels.

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional and the Gibbs-Boltzmann entropy func­tional. In this paper we study the asymptotic behavior of the dynamical systems which describe their approximation of the Fokker-Planck equation and characterize the limit as a solution to a class of variational problems. We also give a simple approach in a one-dimensional case.

In this paper we propose a two dimensional random crystalline algorithm for Gauss cur­vature flow.

開始ページ、終了ページ: 冊子体のページ付け

In this paper we discuss a class of Markov marginal problems (MMP). By MMP, we mean the problem to construct a Markov process with given (marginal) constraints on the path space. As an application we consider Markov optimal control problems.

Since 2004, there is a growing awareness of the risks that tsunamis pose to coastal communities globally. Despite the fact that these events were already an intrinsic part of the culture of some countries such as Chile and Japan, many other places had virtually not heard about such phenomenon before 2004. Nevertheless, the frequent reoccurrence of major tsunamis in recent years has led to the emergence of a ???tsunami culture??? in many areas of the world, which has resulted in increased awareness, disaster preparedness and willingness of local populations to evacuate when the threat of these events arises. However, evacuation during a tsunami is still not successfully carried out by the different elements of society, pointing to lack of awareness, an over-reliance in defence mechanisms or lacking in the transmitting of knowledge from previous events. This paper will explore these cultural issues using as a basis questionnaires carried out by the authors during their own field visits to the last three major events (Chile in 2009, Indonesia in 2010 and Japan in 2011), and interpret these through the willingness of coastal communities to build protection measures along the shore and the impact that these can have on sustainable development. The existence of a ???traditional tsunami culture??? will be explored through an analysis of the existence of multi-layer safety system constructed by previous generations, and whether this is being preserved nowadays or past lessons are being forgotten.