on l_p norms of multivariate density estimators central limit theorems are proven for l p norms 1 leq p infty of multivariate density estimators

mass transshipment problems and ideal metrics abstract the monge kantorovich mass transshipment problem is to minimize the total cost r 2n c x y d b x y over all transshipments b that satisfy the balancing condition b r n b r n p q p and q are viewed as initial and final mass distributions respectively and c x y is a cost function the dual form of the problem was given by kantorovich and rubinstein 1958 for p and q having bounded support and the general case was considered in lecture 20 of dudley 1976 we extend these results studying more general transshipment problems based on higher order differences a new class of ideal metrics arises from our version of the monge kantorovich problem and a dual representation for these metrics is obtained

the bm l _ mathbf 1 norm density estimator process the notion of an l1 norm density estimator process indexed by a class of kernels is introduced then a functional central limit theorem and a glivenko cantelli theorem are established for this process while assembling the necessary machinery to prove these results a body of poissonization techniques and restricted chaining methods is developed which is useful for studying weak convergence of general processes indexed by a class of functions none of the theorems imposes any condition at all on the underlying lebesgue density f also somewhat unexpectedly the distribution of the limiting gaussian process does not depend on f

trajectory tracking problem causal solutions for non linear time delay systems the trajectory tracking problem is considered for a general class of non linear time delay systems the existence of causal static state feedback solutions is investigated within an algebraic approach two classes of causal static compensators are considered that either involve delayed dynamics or not sufficient conditions are derived which are weaker than the ones existing in the current literature these results are innovative for both linear and non linear time delay systems the most advanced results do not imply a maximal loss of observability in opposition to more standard solutions

a class of quasilinear stochastic partial differential equations of mckean vlasov type with mass conservation a system ofn particles inr d with mean field interaction and diffusion is considered assuming adiabatic elimination of the momenta the positions satisfy a stochastic ordinary differential equation driven by brownian sheets microscopic equation where all coefficients depend on the position of the particles and on the empirical mass distribution process this empirical mass distribution process satisfies a quasilinear stochastic partial differential equation spde this spde mezoscopic equation is solved for general measure valued initial conditions by extending the empirical mass distribution process from point measure valued initial conditions with total mass conservation starting with measures with densities inl 2 r d dr wheredr is the lebesgue measure the solution will have densities inl 2 r d dr and strong uniqueness in the ito sense is obtained finally it is indicated how to obtain macroscopic partial differential equations as limits of the so constructed spde s

projection method i convergence and numerical boundary layers this is the first of a series of papers on the subject of projection methods for viscous incompressible flow calculations the purpose of these papers is to provide a thorough understanding of the

macroscopic limits for stochastic partial differential equations of mckean vlasov type a class of quasilinear stochastic partial differential equations spdes driven by spatially correlated brownian noise is shown to become macroscopic i e deterministic as the length of the correlations tends to 0 the limit is the solution of a quasilinear partial differential equation the quasilinear spdes are obtained as a continuum limit from the empirical distribution of a large number of stochastic ordinary differential equations sodes coupled though a mean field interaction and driven by correlated brownian noise the limit theorems are obtained by application of a general result on the convergence of exchangeable systems of processes we also compare our approach to sodes with the one introduced by kunita

global exponential stability of impulsive integro differential equation abstract in this paper an impulsive integro differential equation is considered by establishing an integro differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive integro differential equation are obtained the results extend and improve the earlier publications an example is given to demonstrate the effectiveness of the theory

a positivity based approach to delay dependent stability of systems with large time varying delays abstract in this paper we propose new explicit tests for positivity and exponential stability of systems with large time varying delays our approach is based on nonoscillation of solutions of the corresponding diagonal scalar delay differential equations numerical examples illustrate the efficiency of the results

stability conditions of delay differential systems sufficient conditions of asymptotic stability independent of delay of both the retarded and neutral types of delay differential systems are obtained the main results are based on the sufficient conditions under which the roots of the determinant of a given l l complex matrix polynomial lie either in the open left half plane or inside the unit circle therefore the explicit computation of the determinant polynomial is not required

stability analysis of nonlinear neutral functional differential equations we present a novel approach to analyze the exponential stability of nonlinear neutral functional differential equations our approach is simple and based on a system transformation the comparison principle and the spectral properties of metzler matrices consequently we derive some new explicit criteria for the exponential stability of general nonlinear neutral functional differential equations it is important to note that our approach leads to both delay dependent and delay independent stability criteria several illustrative examples with simulations and a brief comparison between the obtained results with some existing results in the literature are presented

on some limit theorems for continued fractions as a consequence of previous results on anixing random variables some functional limit theorems for quantities related to the continued fraction espansion of a random number in 0 1 are given

testing functional inequalities abstract this paper develops tests for inequality constraints of nonparametric regression functions the test statistics involve a one sided version of l p type functionals of kernel estimators 1 p drawing on the approach of poissonization this paper establishes that the tests are asymptotically distribution free admitting asymptotic normal approximation in particular the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives furthermore we establish conditions under which the tests have nontrivial local power against pitman local alternatives some results from monte carlo simulations are presented

convergence of sums of mixing triangular arrays of random vectors with stationary rows this paper deals with the convergence in distribution to gaussian generalized poisson and infinitely divisible laws of the row sums of certain x or mixing triangular arrays of banach space valued random vectors with stationary rows necessary and sufficient conditions for convergence in terms of individual r v s are proved these include sufficient conditions for the convergence to a stable law of the normalized sums of certain 0 mixing stationary sequences an invariance principle for stationary 0 mixing triangular arrays is given

rate of convergence of transport processes with an application to stochastic differential equations we obtain a rate of convergence of uniform transport processes to brownian motion which we apply to the wong and zakai approximation of stochastic integrals

central limit theorems for lp norms of density estimators let x1 x2 be a sequence of independent identically distributed random variables with a smooth density function f we obtain central limit theorems for int limits infty infty f n t f t p d mu t text 1 underset raise0 3em hbox smash scriptscriptstyle leqslant p infty where fn is a kernel estimate of f and is a measure on the borel sets of

stability analysis for time varying systems with delay using linear lyapunov functionals and a positive systems approach we prove stability of time varying systems with delays using linear lyapunov functionals and positive systems and we provide robustness of the stability with respect to multiplicative uncertainty in the vector fields we allow cases where the delay may be unknown and where the vector fields defining the systems are not necessarily bounded we illustrate our work using a chain of integrators and other examples

nonparametric estimation and inference about the overlap of two distributions this paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques this quantity has been proposed as a measure of economic polarization between two groups anderson 2004 and anderson et al 2010 in ecology it has been used to measure the overlap of species we give the asymptotic distribution theory of our estimator which in some cases of practical relevance is nonstandard due to a boundary value problem we also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider we investigate the finite sample properties of our methods by simulation methods we give an application to the study of polarization within china in recent years using household survey data from two provinces taken in 1987 and 2001 we find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space

remarques sur les m ethodes de projection pour l approximation des equations de navier stokes l objet de cet article est de montrer que les estimations de convergence sur la pression pour les m ethodes de projection d ecrites dans cite shen1 et cite shen2 ne sont pas obtenues correctement car elles sont toutes bas ees sur une in egalit e fausse il semble qu on ait besoin d une convergence en o delta t de la vitesse dans h 2 omega d pour d emontrer les estimations de convergence sur la pression en o delta t la question de savoir si la m ethode de projection a un taux de convergence pour la pression plus elev e que o delta t 1 2 reste ouverte

convergence analysis of the fem approximation of the first order projection method for incompressible flows with and without the inf sup condition in this paper we obtain convergence results for the fully discrete projection method for the numerical approximation of the incompressible navier stokes equations using a finite element approximation for the space discretization we consider two situations in the first one the analysis relies on the satisfaction of the inf sup condition for the velocity pressure finite element spaces after that we study a fully discrete fractional step method using a poisson equation for the pressure in this case the velocity pressure interpolations do not need to accomplish the inf sup condition and in fact we consider the case in which equal velocity pressure interpolation is used optimal convergence results in time and space have been obtained in both cases

exponential stability of nonlinear impulsive neutral integro differential equations abstract in this paper a nonlinear impulsive neutral integro differential equation with time varying delays is considered by establishing a singular impulsive delay integro differential inequality and transforming the n dimensional impulsive neutral integro differential equation to a 2 n dimensional singular impulsive delay integro differential equation some sufficient conditions ensuring the global exponential stability in p c 1 of the zero solution of an impulsive neutral integro differential equation are obtained the results extend and improve the earlier publications an example is also discussed to illustrate the efficiency of the obtained results