blow up of the smooth solution to quantum hydrodynamic models in r d abstract in this paper we firstly investigate the local in time existence of smooth solution for the quantum hydrodynamic models qhd in r d then we prove that any smooth solution of the qhd model which satisfies suitable conditions will blow up in finite time the model can be derived from nonlinear schrodinger equation by a madelung transformation the main idea is based on the construction of approximate solution and energy inequality

weighted classical variogram estimation for data with clustering the classical variogram estimate is convenient but can be unacceptably variable improved estimators are possible especially when the locations of the available data are highly clustered using a simple theoretical example we demonstrate that weighting can dramatically increase the efficiency of classical variogram estimates from clustered data we give expressions for the weights that lead to minimal variance estimators and indicate some obstacles to the use of these weights we then introduce a simple iterative weighting scheme intended to approximate optimal weighting we apply the new weighting to the example that motivated this research estimating the variogram of home radon levels and demonstrate its performance in a simulation study

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

least squares variogram fitting by spatial subsampling summary least squares methods are popular for fitting valid variogram models to spatial data the paper proposes a new least squares method based on spatial subsampling for variogram model fitting we show that the method proposed is statistically efficient among a class of least squares methods including the generalized least squares method further it is computationally much simpler than the generalized least squares method the method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation an extension of the method proposed to a class of spatial regression models is illustrated with a real data example results from a simulation study on finite sample properties of the method are also reported

joint composite estimating functions in spatiotemporal models summary modelling of spatiotemporal processes has received considerable attention in recent statistical research however owing to the high dimensionality of the data the joint modelling of spatial and temporal processes presents a great computational challenge in both likelihood based and bayesian approaches we propose a joint composite estimating function approach to estimating spatiotemporal covariance structures this substantially reduces the computational complexity and is more efficient than existing composite likelihood methods the novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial temporal and spatiotemporal cross pairs which results in overidentified estimating functions thus we form a joint inference function in a spirit that is similar to hansen s generalized method of moments we show that under practical scenarios the estimator proposed is consistent and asymptotically normal simulation studies prove that our method performs well in finite samples finally we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates pm10 in the north eastern usa over a 32 month period

nonparametric estimation of the moments of a general statistic computed from spatial data abstract a statistic s is computed on spatially indexed data x i i d where d is a finite subset of the integer lattice z2 we propose a simple nonparametric method for estimating the moments e g variance skewness of s d using only the observed data at hand the method uses replicates of s computed on smaller subsets of d no explicit knowledge of the underlying spatial dependence mechanism is needed and the marginal distribution of x i may also be unknown the shape of d can be quite irregular and s is allowed to be a general statistic the proposed estimator is shown to be consistent and asymptotically normal under mild conditions on s d and mixing conditions on the strength of spatial dependence as a numerical example the estimator is used in assessing the geographic clumping of cancer deaths in the united states

on left invariant brownian motions and heat kernels of nilpotent lie groups left invariant brownian motions on nilpotent lie groups are studied their characterization is given through ito or stratonovich stochastic differential equations their generators are exhibited and the associated heat semigroups are studied a reduction formula is given for these semigroups and their kernels as integrals of products of normalized random gaussian densities

existence and asymptotic behavior of multi dimensional quantum hydrodynamic model for semiconductors this paper is devoted to the study of the existence and the time asymptotic of multi dimensional quantum hydrodynamic equations for the electron particle density the current density and the electrostatic potential in spatial periodic domain the equations are formally analogous to classical hydrodynamics but differ in the momentum equation which is forced by an additional nonlinear dispersion term due to the quantum bohm potential and are used in the modelling of quantum effects on semiconductor devices we prove the local in time existence of the solutions in the case of the general nonconvex pressure density relation and large and regular initial data furthermore we propose a subsonic type stability condition related to one of the classical hydrodynamical equations when this condition is satisfied the local in time solutions exist globally in time and converge time exponentially toward the corresponding steady state since for this problem classical methods like for instance the friedrichs theory for symmetric hyperbolic systems cannot be used we investigate via an iterative procedure an extended system which incorporates the one under investigation as a special case in particular the dispersive terms appear in the form of a fourth order wave type equation

positive solutions to singular second and third order differential equations for quantum fluids we analyze a quantum trajectory model given by a steady state hydrodynamic system for quantum fluids with positive constant temperature in bounded domains for arbitrary large data the momentum equation can be written as a dispersive third order equation for the particle density where viscous effects are incorporated the phenomena that admit positivity of the solutions are studied the cases one space dimensional dispersive or non dispersive viscous or non viscous are thoroughly analyzed with respect to positivity and existence or non existence of solutions all depending on the constitutive relation for the pressure law we distinguish between isothermal linear and isentropic power law pressure functions of the density it is proved that in the dispersive non viscous model a classical positive solution only exists for small positive particle current densities both for the isentropic and isothermal case uniqueness is also shown in the isentropic subsonic case when the pressure law is strictly convex however we prove that no weak isentropic solution can exist for large current densities the dispersive viscous problem admits a classical positive solution for all current densities both for the isentropic and isothermal case with an ultra diffusion condition

blow up of spherically symmetric smooth solutions to quantum hydrodynamic models abstract we establish several results about the blow up of the spherically symmetric smooth solutions to the initial boundary value problem of quantum hydrodynamic models under some assumptions that a weighed functional associated with the initial momentum is large enough to develop singularities

blow up of the smooth solution to the ibvp of three dimensional quantum hydrodynamic models abstract the initial boundary value problem for three dimensional quantum hydrodynamic models is considered outside a unit ball it is proved that the smooth solution will blow up in a finite time provided that a weighed functional associated with the initial momentum is large

estimating space and space time covariance functions for large data sets a weighted composite likelihood approach in this article we propose two methods for estimating space and space time covariance functions from a gaussian random field based on the composite likelihood idea the first method relies on the maximization of a weighted version of the composite likelihood function while the second one is based on the solution of a weighted composite score equation this last scheme is quite general and could be applied to any kind of composite likelihood an information criterion for model selection based on the first estimation method is also introduced the methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency the effectiveness of the methods is illustrated through examples simulation experiments and by analyzing a dataset on ozone measurements

a cameron martin type quasi invariance theorem for brownian motion on a compact riemannian manifold abstract let m be a compact manifold without boundary o be a fixed base point in m g be a riemannian metric on m and be a g compatible covariant derivative on tm the tangent space to m assume the torsion t of satisfies the skew symmetry condition g t x y y 0 for all vector fields x and y on m for example take to be the levi civita covariant derivative on m g also let denote the wiener measure on w0 m c 0 1 m 0 o and let h s denote stochastic parallel translation relative to along the path w0 m up to time s 0 1 given a c1 function h 0 1 t0m it is shown that the differential equation t h t h with initial condition 0 id w m w m has a solution r maps w m w m the measurable maps from w m to w m this function is a flow on w m i e for all t r t t furthermore t has the quasi invariance property the law t of t with respect to the wiener measure is equivalent to for all t r this result is used to prove an integration by parts formula for the h derivative hf defined by h f d dt 0 f t where f is a c2 cylinder function on w m

formation of singularities in three dimensional compressible fluids presented are several results on the formation of singularities in solutions to the three dimensional euler equations for a polytropic ideal fluid under various assumptions on the initial data in particular it is shown that a localized fluid which is initially compressed and outgoing on average will develop singularities regardless of the size of the initial disturbance

prediction of spatial cumulative distribution functions using subsampling abstract the spatial cumulative distribution function scdf is a random function that provides a statistical summary of a random field over a spatial domain of interest in this article we develop a spatial subsampling method for predicting an scdf based on observations made on a hexagonal grid similar to the one used in the environmental monitoring and assessment program of the u s environmental protection agency we show that under quite general conditions the proposed subsampling method provides accurate data based approximations to the sampling distributions of various functionals of the scdf predictor in particular it produces estimators of different population characteristics such as the quantiles and weighted mean integrated squared errors of the empirical predictor as an illustration we apply the subsampling method to construct large sample prediction bands for the scdf of an ecological index for foliage condition of red maple trees in the state of maine

formation of singularities in solutions to nonlinear hyperbolic equations on etudie des systemes de lois de conservation hyperboliques et d equations d ondes completement non lineaires

blow up of solutions to quantum hydrodynamic models in half space in this paper we prove that any smooth solutions of quantum hydrodynamic model which satisfies suitable conditions will blow up in finite time in half space this model can be considered as the compressible euler equation with quantum potential the main ideal is based on the construction of energy inequality

resampling methods for spatial regression models under a class of stochastic designs in this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a possibly nonuniform stochastic design and are irregularly spaced it is shown that the natural extension of the existing block bootstrap methods for grid spatial data does not work for irregularly spaced spatial data under nonuniform stochastic designs a variant of the blocking mechanism is proposed it is shown that the proposed block bootstrap method provides a valid approximation to the distribution of a class of m estimators of the spatial regression parameters finite sample properties of the method are investigated through a moderately large simulation study and a real data example is given to illustrate the methodology

point and interval estimation of variogram models using spatial empirical likelihood we present a spatial blockwise empirical likelihood method for estimating variogram model parameters in the analysis of spatial data on a grid the method produces point estimators that require no spatial variance estimates to compute unlike least squares methods for variogram fitting but are as efficient as the best least squares estimator in large samples our approach also produces confidence regions for the variogram without requiring knowledge of the full joint distribution of the spatial data in addition the empirical likelihood formulation extends to spatial regression problems and allows simultaneous inference on both spatial trend and variogram parameters we examine the asymptotic behavior of the estimator analytically and investigate its behavior in finite samples through simulation studies

blowup of smooth solutions to the compressible navier stokes equation with compact density we present a sufficient condition on the blowup of smooth solutions to the compressible navier stokes equations in arbitrary space dimensions with initial density of compact support as an immediate application it is shown that any smooth solutions to the compressible navier stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support and an upper bound which depends only on the initial data on the blowup time follows from our elementary analysis immediately another implication is that there is no global small decay in time or even bounded in the case that all the viscosity coefficients are positive smooth solutions to the compressible navier stokes equations for polytropic fluids no matter how small the initial data are as long as the initial density is of compact support this is in contrast to the classical theory of global existence of small solutions to the same system with initial data being a small perturbation of a constant state that is not a vacuum the blowup of smooth solutions to the compressible euler system with initial density and velocity of compact support is a simple consequence of our argument 1998 john wiley sons inc

variance estimation for statistics computed from spatial lattice data summary a statistic s is computed on spatially indexed data x i e d where d is a finite subset of the integer lattice 22 we propose a method for estimating the variance and other moments of s by using only the data the set d may be irregularly shaped the statistic s may be arbitrarily complicated and no distributional assumptions marginal or joint are necessary the method uses the statistic computed on overlapping subshapes of d as replicates of s the estimator is simply the sample variance of the standardized replicates we demonstrate c2 consistency of the estimator under mild conditions on s and the strength of spatial dependence a rate of convergence is also given giving guidance into the appropriate choice of subshape size and the estimator is illustrated in two data examples

absolute continuity of heat kernel measure with pinned wiener measure on loop groups let t 0 k be a connected compact lie group equipped with an ad k invariant inner product on the lie algebra of k associated to this data are two measures 0 t and t 0 on l k the space of continuous loops based at e e k the measure 0 t is pinned wiener measure with variance t while the measure 0 t is a heat kernel measure on l k the measure 0 t is constructed using a k valued brownian motion while the measure 0 t is constructed using a l k valued brownian motion in this paper we show that 0 t is absolutely continuous with respect to 0 t and the radon nikodym derivative d 0 t d 0 t is bounded

on least squares fitting for stationary spatial point processes summary the k function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability in this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the k function by using subsampling we demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures this is done through asymptotic theory simulation experiments and an application to a data set on long leaf pine trees

a general resampling scheme for triangular arrays of alpha mixing random variables with application to the problem of spectral density estimation in 1989 kunsch introduced a modified bootstrap and jackknife for a statistic which is used to estimate a parameter of the m dimensional joint distribution of stationary and alpha mixing observations the modification amounts to resampling whole blocks of consecutive observations or deleting whole blocks one at a time liu and singh independently proposed in 1988 the same technique for observations that are m dependent however many time series statistics notably estimators of the spectral density function involve parameters of the whole infinite dimensional joint distribution and hence do not fit in this framework in this report we generalize the moving blocks resampling scheme of kunsch and liu and singh a still modified version of the nonparametric bootstrap and jackknife is seen to be valid for general linear statistics that are asymptotically normal and consistent for a parameter of the whole joint distribution we then apply this result to the problem of estimation of the spectral density

on sample reuse methods for dependent data we suggest a sample reuse method for dependent data based on a cross between the block bootstrap and richardson extrapolation instead of simulating a same size resample by resampling blocks and placing them end to end it analyses the blocks directly and employs a variant of richardson extrapolation to adjust for block size a simple empirical rule also based on richardson extrapolation is suggested for empirically selecting the block size performance in the contexts of distribution and bias estimation is discussed via theoretical analysis and numerical simulation

filtering with observations on a riemannian symmetric space the point under discussion in this paper refers to a problem of filtering in which observation y of a system state x is a process with values in a symmetric space m the observation is a brownian motion transformed by an isometry of m depending on the state it takes its values in manifold m and its multiplicative formulation is nonstandard in many physical situations e g mechanics robotics spatial fields the filtering problems are naturally set up in manifolds as well for the signal and the observation the reference probability method is used to construct the model then filtering equations are deduced these comply with the conditional law according to its observation unique characterization of this conditional law is given last two examples are investigated first the multivariate case the observation y is in mathbb r d so that y t sigma t x w t h t x where w is a multivariate brownian motion sigma a rotation and h a translation are absolutely continuous with respe

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field

a generalized formula of ito and some other properties of stochastic flows a stochastic differential equation with smooth coefficients is considered which defines a continuous flow t of c 8 mappings of rd in rd if zt is a continuous semi martingale t zt s is proved to be a semi martingale for which an ito type formula is established it is shown that a s for any t t is an onto diffeomorphism if zt is a continuous semi martingale t 1 zt is proved to be a semi martingale whose ito decomposition is explicitly found