on viscosity and fluctuation dissipation in exclusion processes we consider the asymmetric simple exclusion process we review some results in dimension d 3 concerning the fluctuation dissipation theorem and we prove regularity of viscosity coefficients

elliptic problems with nonlinearities indefinite in sign abstract let r n n 3 be a bounded open set with smooth boundary and r we study the dirichlet problem formula with 1 q p and h k l nonnegative functions we prove existence nonexistence and multiplicity results depending on and according to the integrability properties of the ratio k p 1 h q 1

lattice gas model in random medium and open boundaries hydrodynamic and relaxation to the steady state we consider a lattice gas interacting by the exclusion rule in the presence of a random field given by i i d bounded random variables in a bounded domain in contact with particles reservoir at different densities we show in dimensions d 3 that the rescaled empirical density field almost surely with respect to the random field converges to the unique weak solution of a quasilinear parabolic equation having the diffusion matrix determined by the statistical properties of the external random field and boundary conditions determined by the density of the reservoir further we show that the rescaled empirical density field in the stationary regime almost surely with respect to the random field converges to the solution of the associated stationary transport equation

diffusive limit of a tagged particle in asymmetric simple exclusion processes invariance principles are proved under diffusive scaling for the centered position of a tagged particle in the simple exclusion process with asymmetric nonzero drift jump probabilities in dimensions d 3 the method of proof is by martingale techniques which rely on the fact that symmetric random walks are transient in high dimensions c 2000 john wiley sons inc

existence and multiplicity of solutions for a nonlocal problem with critical sobolev exponent abstract in this work we are interested in considering the following nonlocal problem a b u 2 d x u u 2 2 u u q 2 u x u 0 x where r n n 4 is a smooth bounded domain a 0 b 0 1 q 2 0 and 2 2 n n 2 is the critical sobolev exponent by using the variational method and the critical point theorem some existence and multiplicity results are obtained

nontrivial solutions of kirchhoff type problems via the yang index abstract we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the yang index and critical groups

uniqueness and non degeneracy of positive radial solutions for quasilinear elliptic equations with exponential nonlinearity abstract we are concerned with the uniqueness and non degeneracy result of positive solutions for a class of quasilinear elliptic equations with exponential nonlinearity we convert a quasilinear elliptic equation into a semilinear one and study precise correspondences between two equations we show the uniqueness and the non degeneracy of positive solutions by analyzing the converted semilinear problem

fluctuation dissipation equation of asymmetric simple exclusion processes we consider asymmetric simple exclusion processes on the lattice zopf d in dimension d 3 we denote by l the generator of the process the lattice gradient the configuration and w the current of the dynamics associated to the conserved quantity we prove that the fluctuation dissipation equation w lu d has a solution for some function u and some constant d identified to be the diffusion coefficient intuitively lu represents rapid fluctuation and this equation describes a decomposition of the current into fluctuation and gradient of the density field representing the dissipation using this result we proved rigorously that the green kubo formula converges and it can be identified as the diffusion coefficient

multiple positive solutions to a class of kirchhoff equation on r3 with indefinite nonlinearity abstract we study the existence and multiplicity of positive solutions to a class of kirchhoff equation 1 b r 3 u x 2 d x u x u x v x u x p 2 u x k x u x u x u h 1 r 3 when v x is sign changing in r 3 we prove that there is 0 such that the kirchhoff equation possesses at least one positive solution for 0 1 and at least two positive solutions for 1 1 here 1 is the first eigenvalue of u u k x u u h 1 r 3 a positive eigenfunction corresponding to 1 is denoted by e 1 an interesting phenomena is that the term b r 3 u 2 d x u can be used to compete with the indefinite nonlinearity and we do not assume the condition r 3 v x e 1 p d x 0 which has been shown to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearity alama and tarantello 1993

tests of linear hypotheses and l 1 estimation statistics of a linear hypothesis in the standard linear model these test statistics which correspond to wald likelihood ratio and lagrange multiplier tests are shown to have the same limiting chi square behavior under mild regularity conditions on design and the distribution of errors the asymptotic theory of the tests is derived for a large class of error distributions thus in huber s 10 terminology we investigate the behavior of the likelihood ratio test under non standard conditions the asymptotic efficiency of the 11 tests involves a modest sacrifice of power compared to classical tests in cases of strictly gaussian errors but may yield large efficiency gains in non gaussian situations the lagrange multiplier test seems particularly attractive from a computational standpoint we derive the asymptotic distribution of the three alternative 11 test statistics for a simple linear exclusion hypothesis extension of these results to hypotheses of the form r 8 r is a straightforward exercise when the density of the error distribution is strictly positive at the median all three test statistics have the same limiting central x2 behavior at the null and noncentral x2 behavior for local alternatives to the null when the variance of the error distribution is bounded analogous results are well known for classical forms of the wald likelihood ratio and lagrange multipler tests based on least squares methods see for example silvey 18 and the discussion in section 4 below

existence of solutions for a higher order kirchhoff type problem with exponential critical growth abstract a higher order kirchhoff type equation r 2 m m u 2 0 m 1 a x u 2 d x m u 0 m 1 1 a x u f x u x h x in r 2 m is considered in this paper we assume that the nonlinearity of the equation has exponential critical growth and prove that for a positive which is small enough there are two distinct nontrivial solutions to the equation when 0 we also prove that the equation has a nontrivial mountain pass type solution

infinitely many small solutions for the kirchhoff equation with local sublinear nonlinearities abstract we study the following nonlinear kirchhoff equation on the whole space 1 b r 3 u 2 v x u 2 d x u v x u f x u in r 3 where b 0 is a constant and the nonlinear term f x u is only locally defined for u small and satisfies some mild conditions it is proved that the above problem admits infinity many weak solutions provided that some additional assumptions are satisfied moreover we show that these solutions tend to zero in l r 3 our method relies upon a variant of the symmetric mountain pass lemma due to kajikiya and moser iteration method

a multiplicity result for some nonlocal eigenvalue problem with exponential growth condition in this paper a new variational tool is used to establish a multiplicity result for some equation containing a nonlocal term and involving the n laplacian operator and whose nonlinear term can have a critical exponential growth the equation has a nonvariational nature

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

multiple solutions for p kirchhoff equations in rn abstract in this paper we prove the existence of multiple ground state solutions for the nonhomogeneous p kirchhoff elliptic equation 0 1 m r n u p v x u p d x p u v x u p 2 u f x u g x in r n where v x c r n and v x as x the nonlinear function f x u is continuous and satisfies some conditions the solutions will be obtained by the mountain pass theorem ekeland s variational principle and krasnoselskii s genus theory in struwe 2000 1

infinitely many positive solutions for kirchhoff type problems abstract this paper is concerned with the existence of infinitely many positive solutions to a class of kirchhoff type problem a b u 2 d x u f x u in and u 0 on where is a smooth bounded domain of r n a b 0 0 and f r r is a caratheodory function satisfying some further conditions we obtain a sequence of a e positive weak solutions to the above problem tending to zero in l with f being more general than that of k perera z zhang nontrivial solutions of kirchhoff type problems via the yang index j differential equations 221 2006 246 255 z zhang k perera sign changing solutions of kirchhoff type problems via invariant sets of descent flow j math anal appl 317 2006 456 463

existence and multiplicity of solutions for fractional schrodinger kirchhoff equations with trudinger moser nonlinearity abstract we study the existence and multiplicity of solutions for a class of fractional schrodinger kirchhoff type equations with the trudinger moser nonlinearity more precisely we consider m u n s n s s u v x u n s 1 u f x u h x u p 2 u in r n u r 2 n u x u y n s x y 2 n d x d y r n v x u n s d x s n where m 0 0 is a continuous function s 0 1 n 2 0 is a parameter 1 p n s s is the fractional n s laplacian v r n 0 is a continuous function f r n r r is a continuous function and h r n 0 is a measurable function first using the mountain pass theorem a nonnegative solution is obtained when f satisfies exponential growth conditions and is large enough and we prove that the solution converges to zero in w v s n s r n as then using the ekeland variational principle a nonnegative nontrivial solution is obtained when is small enough and we show that the solution converges to zero in w v s n s r n as 0 furthermore using the genus theory infinitely many solutions are obtained when m is a special function and is small enough we note that our paper covers a novel feature of kirchhoff problems that is the kirchhoff function m 0 0

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

on a singular and nonhomogeneous n laplacian equation involving critical growth abstract in this paper we apply minimax methods to obtain existence and multiplicity of weak solutions for singular and nonhomogeneous elliptic equation of the form n u f x u x a h x in where u w 0 1 n n u div u n 2 u is the n laplacian a 0 n is a smooth bounded domain in r n n 2 containing the origin and h w 0 1 n w 1 n is a small perturbation h 0 motivated by a singular trudinger moser inequality we study the case when f x s has the maximal growth on s which allows to treat this problem variationally in the sobolev space w 0 1 n

segmented model selection in quantile regression using the minimum description length principle this article proposes new model fitting techniques for quantiles of an observed data sequence including methods for data segmentation and variable selection the main contribution however is in providing a means to perform these two tasks simultaneously this is achieved by matching the data with the best fitting piecewise quantile regression model where the fit is determined by a penalization derived from the minimum description length principle the resulting optimization problem is solved with the use of genetic algorithms the proposed fully automatic procedures are unlike traditional break point procedures not based on repeated hypothesis tests and do not require unlike most variable selection procedures the specification of a tuning parameter theoretical large sample properties are derived empirical comparisons with existing break point and variable selection methods for quantiles indicate that the new procedures work well in practice

large deviation principle for interacting brownian motions we prove the large deviation principle for the empirical process in a system of locally interacting brownian motions in the nonequilibrium such a phenomenon has been proven only for two lattice systems the symmetric simple exclusion process and the zero range process therefore we have achieved the third result in this context and moreover the first result for the diffusion type interacting particle system 2016 wiley periodicals inc

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

multiple nontrivial solutions to a pp kirchhoff equation abstract in this paper morse theory is used to show the existence of nontrivial solutions to the nonlocal p kirchhoff type quasilinear elliptic equation m u p d x p 1 p u f x u in a smooth bounded domain r n with dirichlet boundary condition

finite dimensional approximation of the self diffusion coefficient for the exclusion process we show that for the symmetric simple exclusion process on z d the self diffusion coefficient of a tagged particle is stable when approximated by simple exclusion processes on large periodic lattices the proof depends on a similar stability property of the asymptotic variance of additive functionals of mean 0 this requires establishing a property for the dirichlet space known as the liouville d property

multiplicity of solutions for a class of quasilinear equations with exponential critical growth abstract this paper deals with some results of existence and multiplicity of solutions for quasilinear problems involving the n laplacian operator when the nonlinearity has exponential critical growth to obtain our results we utilize ekeland variational principle mountain pass theorem and inequalities of the type trudinger moser bounded and unbounded domains are considered

on the sector condition and homogenization of diffusions with a gaussian drift abstract in this paper we present the functional central limit theorem for a class of markov processes whose l 2 generator satisfies the so called graded sector condition we apply the result to obtain homogenization theorems for certain classes of diffusions with a random gaussian drift additionally we present a result concerning the regularity of the effective diffusivity tensor with respect to the parameters related to the statistics of the drift the abstract central limit theorem see theorem 2 2 is obtained by applying the technique used in sethuraman et al comm pure appl math 53 2000 972 to the case of infinite particle systems

regularity of the diffusion coefficient matrix for lattice gas reversible under gibbs measures with mixing condition in this paper we obtain that the diffusion coefficient matrix for lattice gas reversible under gibbs measures with mixing condition is continuously differentiable with respect to order parameter

singular perturbed kirchhoff type problem with critical exponent abstract in the present paper we consider the following kirchhoff type problem with critical exponent e 2 a e b r 3 u 2 d x u v x u f u in r 3 u h 1 r 3 by variational methods we show the existence of the positive solutions concentrating around global minima of the potential v x as e 0 we do not need the monotonicity of the function f 3

symmetric simple exclusion process regularity of the self diffusion coefficient we prove that the self diffusion coefficient of a tagged particle in the symmetric exclusion process in zd which is in equilibrium at density is of class c as a function of in the closed interval 0 1 the proof provides also a recursive method to compute the taylor expansion at the boundaries

bent line quantile regression with application to an allometric study of land mammals speed and mass summary quantile regression which models the conditional quantiles of the response variable given covariates usually assumes a linear model however this kind of linearity is often unrealistic in real life one situation where linear quantile regression is not appropriate is when the response variable is piecewise linear but still continuous in covariates to analyze such data we propose a bent line quantile regression model we derive its parameter estimates prove that they are asymptotically valid given the existence of a change point and discuss several methods for testing the existence of a change point in bent line quantile regression together with a power comparison by simulation an example of land mammal maximal running speeds is given to illustrate an application of bent line quantile regression in which this model is theoretically justified and its parameters are of direct biological interests

positive solution for a superlinear kirchhoff type problem with a parameter abstract this paper is devoted to a nonlinear kirchhoff type problem depending on a real function and a nonnegative parameter on a smooth bounded domain of r n n 2 we show that if the nonlinearity is subcritical and superlinear at zero and infinity then there exists a positive value such that the kirchhoff type problem has at least one positive solution for any value of the parameter less than the positive value the main tools are variational methods critical point theory and iterative techniques

sign changing and multiple solutions of kirchhoff type problems without the p s condition abstract the existence of nontrivial solutions of kirchhoff type equations is an important nonlocal quasilinear problem in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4 superlinear kirchhoff type problems without the p s condition one concerning the existence of a nontrivial solution and the other one concerning the existence of sign changing solutions and multiple solutions a b u 2 u f x u in u 0 on

sign changing solutions of kirchhoff type problems via invariant sets of descent flow we obtain sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow

on multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in rn abstract in this work we study the existence multiplicity and concentration of positive solutions for the following class of quasilinear problems n n u v x u n 2 u f u in r n u x 0 x r n where n u is the n laplacian operator is a positive parameter n 2 v r n r is a continuous function and f r r is a c 1 function having critical exponential growth

multiplicity of solutions for p x polyharmonic elliptic kirchhoff equations abstract in this paper we establish the existence of an unbounded sequence of solutions for a class of quasilinear elliptic p x polyharmonic kirchhoff equations including the new delicate degenerate case not yet covered in the literature the main tool is the symmetric mountain pass theorem of ambrosetti and rabinowitz

hydrodynamic limit of asymmetric exclusion processes under diffusive scaling in d 3 we consider the asymmetric exclusion process we start from a profile which is constant along the drift direction and prove that the density profile under a diffusive rescaling of time converges to the solution of a parabolic equation

existence and multiplicity of solutions to equations of n laplacian type with critical exponential growth in rn in this paper we deal with the existence of solutions to the nonuniformly elliptic equation of the form 0 1 div a x u v x u n 2u f x u x eh x in rn when f rn r r behaves like exp u n n 1 when u and satisfies the ambrosetti rabinowitz condition in particular in the case of n laplacian i e a x u u n 2 u we obtain multiplicity of weak solutions of 0 1 moreover we can get the nontriviality of the solution in this case when e 0 finally we show that the main results remain true if one replaces the ambrosetti rabinowitz condition on the nonlinearity by weaker assumptions and thus we establish the existence and multiplicity results for a wider class of nonlinearity see section 7 for more details

multiple solutions for n kirchhoff type problems with critical exponential growth in rn abstract in this paper we consider a class of nonlocal n kirchhoff type problems involving a nonlinearity term having critical exponential growth by applying variational methods together with trudinger moser inequality in whole r n we obtain the existence of at least two positive solutions

existence and concentration of sign changing solutions to kirchhoff type system with hartree type nonlinearity abstract in this paper we discuss the existence and the concentration of sign changing solutions to a class of kirchhoff type systems with hartree type nonlinearity in r 3 by the minimization argument on the sign changing nehari manifold and a quantitative deformation lemma we prove that the system has a sign changing solution moreover concentration behaviors of sign changing solutions are obtained when the coefficient of the potential function tends to infinity specially our results cover general schrodinger equations kirchhoff equations and schrodinger poisson systems

some properties of the diffusion coefficient for asymmetric simple exclusion processes the hydrodynamical limit of asymmetric simple exclusion processes is given by an inviscid burgers equation and its next order correction is given by the viscous burgers equation the diffusivity can be characterized by an abstract formulation in a hilbert space with the inverse of the diffusivity characterized by a variational formula alternatively it can be described by the green kubo formula we give arguments that these two formulations are equivalent we also derive two other variational formulas one for the inverse of the diffusivity and one for the diffusivity itself characterizing diffusivity as a supremum and as an infimum these two formulas also provide an analytic criterion for deciding whether the diffusivity as defined by the linear response theory is symmetric furthermore we prove the continuity of the diffusivity and a few other relations concerning diffusivity and solutions of the euler lagrange equations of these variational problems

approximation of the effective conductivity of ergodic media by periodization this paper is concerned with the approximation of the effective conductivity a associated to an elliptic operator xa x x where for x d d 1 a x is a bounded elliptic random symmetric d d matrix and takes value in an ergodic probability space x writing an x the periodization of a x on the torus tdn of dimension d and side n we prove that for almost all we extend this result to non symmetric operators x a e x x corresponding to diffusions in ergodic divergence free flows a is d d elliptic symmetric matrix and e x an ergodic skew symmetric matrix and to discrete operators corresponding to random walks on d with ergodic jump rates

quantile smoothing splines summary although nonparametric regression has traditionally focused on the estimation of conditional mean functions nonparametric estimation of conditional quantile functions is often of substantial practical interest we explore a class of quantile smoothing splines defined as solutions to

on a class of quasilinear elliptic problems involving trudinger moser nonlinearities abstract in this paper we consider the following class of quasilinear elliptic problems div a x u h x exp 0 u n n 1 f x u in with the dirichlet boundary condition where r n n 2 is a smooth bounded domain and 0 is a positive parameter we assume that there exists a r n r such that a a satisfies some mild conditions h x and f x s are mensurable functions and f x s can enjoy exponential critical growth the approach relies on a fixed point theorem and the trudinger moser inequality