local well posedness for a lotka volterra system in besov spaces this paper is devoted to study local existence uniqueness and continuous dependence upon the initial data of mild solutions for a diffusive non autonomous lotka volterra system initial data are taken in the besov space b p q n

the equivalence of certain heat kernel and green function bounds abstract we show that certain upper and lower bounds on the green function and heat kernel of a second order elliptic operator in a bounded region are equivalent and imply a number of apparently stronger bounds we also show that these bounds are equivalent to the harnack inequality except for peculiar regions and are therefore almost always valid

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

boundary harnack principle for δ δ 2 for d 1 and 2 0 2 consider the family of pseudo differential operators f b 2 b 2 0 1 g on r d that evolves continuously fromto 2 in this paper we establish a uniform boundary harnack principle bhp with explicit boundary decay rate for nonnegative functions which are harmonic with respect to b 2 or equivalently the sum of a brownian motion and an independent symmetric stable process with constant multipleb 1 inc 1 1 open sets here a uniform bhp means that the comparing constant in the bhp is independent of b 2 0 1 along the way a uniform carleson type estimate is established for nonnegative functions which are harmonic with respect to b 2 in lipschitz open sets our method employs a combination of probabilistic and analytic techniques

two sided heat kernel estimates for censored stable like processes in this paper we study the precise behavior of the transition density func tions of censored resurrected stable like processes in c 1 1 open sets in r d where d 1 and 1 2 we first show that the semigroup of the censored stable like process in any bounded lipschitz open set is intrinsically ultracontractive we then establish sharp two sided estimates for the transition density functions of a large class of censored stable like processes in c 1 1 open sets we further obtain sharp two sided estimates for the green functions of these censored stable like processes in bounded c 1 1 open sets

the saddlepoint correction in conditional logistic likelihood analysis summary barndorff nielsen cox 1979 introduced the double saddlepoint approximation to the conditional likelihood function for a structural parameter vector given a sufficient statistic for a nuisance parameter vector this approximation is considered in some detail for the case of multiple logistic regression models with polytomous outcome states it is shown that the profile score with saddlepoint correction yields a simple derivation of an approximation to the mean of a noncentral hypergeometric random variable discussed by levin 1984 and gart 1987 while providing analogous formulae in more general cases and extends to the general case an algorithm of mccullagh 1984 for the approximate calculation of conditional maximum likelihood estimates of log odds ratio regression coefficients from several fourfold tables

well posedness of the cauchy problem for the fractional power dissipative equations abstract this paper studies the cauchy problem for the nonlinear fractional power dissipative equation u t u f u for initial data in the lebesgue space l r r n with either r r d n b 2 d or the homogeneous besov space b p r n with 2 d b n p and 1 p where 0 f u f u or q d f u with q d being a homogeneous pseudo differential operator of order d 0 2 and f u is a function of u which behaves like u b u with b 0

ultracontractivity and the heat kernel for schrodinger operators and dirichlet laplacians abstract abstract connections between integral kernels of positivity preserving semigroups and suitable lp contractivity properties are established then these questions are studied for the semigroups generated by v and h the dirichlet laplacian for an open connected region as an application under a suitable hypothesis sobolev estimates are proved valid up to of the form x c 0 x h k 2 where 0 is the unique positive l2 eigenfunction of h

global well posedness and asymptotic behavior in besov morrey spaces for chemotaxis navier stokes fluids in this work we consider the keller segel system coupled with navier stokes equations in rn for n 2 we prove the global well posedness with small initial data in besov morrey spaces our initial data class extends previous ones found in the literature such as that obtained by kozono miura and sugiyama j funct anal 270 5 1663 1683 2016 it allows us to consider initial cell density and fluid velocity concentrated on smooth curves or at points depending on the spatial dimension self similar solutions are obtained depending on the homogeneity of the initial data and considering the case of a chemical attractant without the degradation rate moreover we analyze the asymptotic stability of solutions at infinity and obtain a class of asymptotically self similar ones in this work we consider the keller segel system coupled with navier stokes equations in rn for n 2 we prove the global well posedness with small initial data in besov morrey spaces our initial data class extends previous ones found in the literature such as that obtained by kozono miura and sugiyama j funct anal 270 5 1663 1683 2016 it allows us to consider initial cell density and fluid velocity concentrated on smooth curves or at points depending on the spatial dimension self similar solutions are obtained depending on the homogeneity of the initial data and considering the case of a chemical attractant without the degradation rate moreover we analyze the asymptotic stability of solutions at infinity and obtain a class of asymptotically self similar ones

symmetrization techniques on unbounded domains application to a chemotaxis system on rn the authors study the parabolic elliptic system on rn u t u u v 0 v v u u 0 u0 a version of the mathematical model of chemotaxis proposed by keller and segel a differential inequality for the quantity s0u t d where u is the decreasing rearrangement of the solution u t with respect to the spatial variable is obtained as a consequence they obtain e g lp bounds of the solution u v on r2 and global in time existence of solutions under the condition r2u0 8 then the solution u v blows up in a finite time compared to the previous work of diaz diaz and nagai adv math sci appl 5 1995 no 2 659 680 mr1361010 96j 35246 where this problem has been considered on bounded domains of rn there are some additional technical difficulties connected with the regularity of the derivative u t

global strong solution to the semi linear keller segel system of parabolic parabolic type with small data in scale invariant spaces abstract we shall show existence of global strong solution to the semi linear keller segel system in r n n 3 of parabolic parabolic type with small initial data u 0 h n r 2 r r n and v 0 h n r r r n for max 1 n 4 r n 2 our method is based on the perturbation of linealization together with the l p l q estimates of the heat semigroup and the fractional powers of the laplace operator as a by product of our method we shall prove the decay property of solutions as the time goes to infinity

simple tests of homogeneity of controls in matched studies consider matched case control studies with a pair of distinguishable controls say neighbourhood and hospital wherein one of the controls may be missing liang and stewart derive an efficient test for the possible difference in controls for the complete data case they suggest inefficient tests for the situation where some triplets are incomplete levin and risch and tibshirani derive efficient tests for the incomplete triplet case by the methods of maximum likelihood estimator wald tests and likelihood ratio tests respectively all these tests require the use of compute algorithms using score theory we derive a simple efficient test for complete triplets which only requires solving a quadratic equation furthermore we show that the usual normal approximation to mcnemar s test is equivalent to the score test and is thus fully efficient as well for incomplete triplets score theory leads to a fully efficient test which only requires the solution of a cubic equation we propose a nearly efficient test which is even more simply computed the example of liang and stewart illustrates application of the results

the boundary behavior of heat kernels of dirichlet laplacians we prove the following complete and qualitatively sharp description of heat kernels g of dirichlet laplacians on bounded c1 1 domains d there exist positive constants c1 c2 and t 0 depending on d such that for x dist x d x y t 1c1tn 2e c2 x y 2 t g x t y 0 x y t 11c1tn 2e x y 2 c2t for all x y d and 0 t are known bounds when d is unbounded are also given

two sided eigenvalue estimates for subordinate processes in domains let x xt t 0 be a symmetric markov process in a state space e and d an open set of e denote by x d the subprocess of x killed upon leaving d let s st t 0 be a subordinator with laplace exponent that is independent of x the processes x xst t 0 and x d x dt t 0 are called the subordinate processes of x and x d respectively under some mild conditions we show that if n n 1 and n n 1 denote the eigenvalues of the generators of the subprocess of x killed upon leaving d and of the process x d respectively then

global solutions for some nonlinear parabolic equations with nonmonotonic peturbations publisher summary this chapter discusses the existence uniqueness and decay property of the solutions of two problems it also presents the sobolev s lemma and gagliardo nirenberg inequality

heat kernel estimates for the fractional laplacian with dirichlet conditions we give sharp estimates for the heat kernel of the fractional laplacian with dirichlet condition for a general class of domains including lipschitz domains

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

heat kernel estimates for jump processes of mixed types on metric measure spaces in this paper we investigate symmetric jump type processes on a class of metric measure spaces with jumping intensities comparable to radially symmetric functions on the spaces the class of metric measure spaces includes the alfors d regular sets which is a class of fractal sets that contains geometrically self similar sets a typical example of our jump type processes is the symmetric jump process with jumping intensity e c 0 x y x y int alpha 1 alpha 2 frac c alpha x y x y d alpha nu d alpha where is a probability measure on alpha 1 alpha 2 subset 0 2 c x y is a jointly measurable function that is symmetric in x y and is bounded between two positive constants and c 0 x y is a jointly measurable function that is symmetric in x y and is bounded between 1 and 2 where either 2 1 0 or 1 2 0 this example contains mixed symmetric stable processes on mathbb r n as well as mixed relativistic symmetric stable processes on mathbb r n we establish parabolic harnack principle and derive sharp two sided heat kernel estimate for such jump type processes

global heat kernel estimates for symmetric jump processes in this paper we study sharp heat kernel estimates for a large class of symmetric jump type processes in r d for all t 0 a prototype of the processes under consideration are symmetric jump processes on r d with jumping intensity

the optimal temporal decay estimates for the fractional power dissipative equation in negative besov spaces in this paper we first generalize a new energy approach developed by guo and wang commun partial differ equations 37 2165 2208 2012 in the framework of homogeneous besov spaces for proving the optimal temporal decay rates of solutions to the fractional power dissipative equation then we apply this approach to the critical and supercritical surface quasi geostrophic equation and the critical keller segel system we show that certain weighted negative besov norm of solutions is preserved along time evolution and obtain the optimal temporal decay rates of the spatial derivatives of solutions by the fourier splitting approach and the interpolation techniques

two sided green function estimates for killed subordinate brownian motions a subordinate brownian motion is a levy process that can be obtained by replacing the time of the brownian motion by an independent subordinator the infinitesimal generator of a subordinate brownian motion is where is the laplace exponent of the subordinator in this paper we consider a large class of subordinate brownian motions without diffusion component and with comparable to a regularly varying function at infinity this class of processes includes symmetric stable processes relativistic stable processes sums of independent symmetric stable processes sums of independent relativistic stable processes and much more we give sharp two sided estimates on the green functions of these subordinate brownian motions in any bounded fat open set d w hend is a bounded c 1 1 open set we establish an explicit form of the estimates in terms of the distance to the boundary as a consequence of such sharp green function estimates we obtain a boundary harnack principle in c 1 1 open sets with explicit rate of decay

approximate conditional inference in generalized linear models on developpe des approximations precises et facilement calculables pour les densites conditionnelles et les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques

saddlepoint approximations of the distribution of the person parameter in the two parameter logistic model large sample theory states the asymptotic normality of the maximum likelihood estimator of the person parameter in the two parameter logistic 2pl model in short tests however the assumption of normality can be grossly wrong as a consequence intended coverage rates may be exceeded and confidence intervals are revealed to be overly conservative methods belonging to the higher order theory more specifically saddlepoint approximations are a convenient way to deal with small sample problems confidence bounds obtained by these means hold the approximate confidence level for a broad range of the person parameter moreover an approximation to the exact distribution permits to compute median unbiased estimates mue that are as likely to overestimate as to underestimate the true person parameter additionally in small samples these mue are less mean biased than the often used maximum likelihood estimator

bartlett s bias correction to the profile score function is a saddlepoint correction summary bartlett s bias correction to the profile score function is proved equal to first order to the leading correction term of the double saddlepoint approximation to the conditional score function in canonical exponential families gart 1985 1987 has pointed out the effectiveness of bartlett s bias correction to the profile score function in approximate conditional binomial likelihood analysis while the leading term in bartlett s 1953 1955 expansion of the bias function ignores terms of order o n 2 the first term correction works well for conditional analysis because as shown in this note in canonical exponential families it agrees with the first correction term of the double saddlepoint approximation to the conditional score function and that approximation is accurate up to terms of order o n

sharp heat kernel estimates for relativistic stable processes in open sets in this paper we establish sharp two sided estimates for the transition densities of relativistic stable processes i e for the heat kernels of the operators m m2 2 in c1 1 open sets here m 0 and 0 2 the estimates are uniform in m 0 m for each fixed m 0 letting m 0 we recover the dirichlet heat kernel estimates for 2 2 in c1 1 open sets obtained in 14 sharp two sided estimates are also obtained for green functions of relativistic stable processes in bounded c1 1 open sets

likelihood calculations for matched case control studies and survival studies with tied death times summary a recursion is presented which permits rapid computation of a conditional likelihood function which arises in matched case control studies and survival studies with tied death times an example with seven parameters and ten large strata the largest of which contains 29 cases and 52 controls illustrates the feasibility of the conditional maximum likelihood solution these methods may be specialized to permit rapid calculation of the conditional maximum likelihood estimate of the common odds ratio for several 2 x 2 tables

methods of estimation in log odds ratio regression models mccullagh s 1984 journal of the royal statistical society series b 46 250 256 approximation to the conditional maximum likelihood estimator in log odds ratio regression models is shown to have negligible asymptotic bias unless the odds ratios are large and the sample sizes in individual 2 x 2 tables are very small in application to two sets of case control data it yields results virtually indistinguishable from those of the conditional analysis a generalization of the mantel haenszel estimator proposed by davis 1985 biometrics 41 487 495 does not approximate the conditional results nearly as well

global well posedness for nonlocal fractional keller segel systems in critical besov spaces abstract in this paper we study keller segel systems with fractional diffusion and a nonlocal term we establish the global existence uniqueness and stability of solutions for systems with small initial data in critical besov spaces our main tools are the l p l q estimates for e t 2 in besov spaces and the perturbation of linearization

explicit constants for gaussian upper bounds on heat kernels on utilise des inegalites logarithmiques de sobolev pour obtenir des bornes superieures gaussiennes sur les noyaux de la chaleur associes a des operateurs d ordre 2 elliptiques et hypoelliptiques

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

dirichlet heat kernel estimates for subordinate brownian motions with gaussian components in this paper we derive explicit sharp two sided estimates for the dirichlet heat kernels in c 1 1 open sets d in r d of a large class of subordinate brownian motions with gaussian components when d is bounded our sharp two sided dirichlet heat kernel estimates hold for all t 0 integrating the heat kernel estimates with respect to the time variable t we obtain sharp two sided estimates for the green functions in bounded c 1 1 open sets of such subordinate brownian motions with gaussian components

well posedness of the cauchy problem for the fractional power dissipative equation in critical besov spaces abstract in this paper we study the cauchy problem for the semilinear fractional power dissipative equation u t u f u for the initial data u 0 in critical besov spaces b 2 r with n 2 2 d b where 0 f u p d u b 1 with p d being a homogeneous pseudo differential operator of order d 0 2 and b 0 being an integer making use of some estimates of the corresponding linear equation in the frame of mixed time space spaces the so called mono norm method which is different from the kato s double norm method fourier localization technique and littlewood paley theory we get the well posedness result in the case n 2

the equivalence of two corrections to the approximate mean of an entry in a contingency table summary stevens 1951 gives approximate expressions for the conditional mean and variance of an entry in a contingency table with fixed marginals cornfield 1956 shows these to be the moments of the asymptotic normal approximation to the noncentral hypergeometric distribution mccullagh 1984 and levin 1984 suggest corrections to the expression for the mean we show that the bias correction preferred by levin for the conditional case is virtually identical to that derived by gart 1985a for the unconditional case this correction is based on bartlett s 1955 general results for score statistics related theory bartlett 1953 yields stevens s approximate variance formula and an expression for the third central moment

simple improvements on cornfield s approximation to the mean of a noncentral hypergeometric random variable summary this note provides some simple improvements to cornfield s asymptotic approximation to the mean of a noncentral hypergeometric random variable simplicity in the sense of avoidance of exact computation in favour of easy approximations derives from an observation of mantel hankey that in a four fold table with all margins fixed the ratio of expected cross products is equal to the odds ratio parameter governing the noncentral distribution of the reference cell the improvements often reduce the relative error of approximation by one or more powers of ten even for tables whose total sample size is as small as two

global and exploding solutions for nonlocal quadratic evolution problems nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered the inertial type nonlinearity is quadratic and nonlocal while the diffusive term also nonlocal is anomalous and fractal i e represented by a fractional power of the laplacian conditions for global in time existence versus finite time blow up are studied self similar solutions are constructed for certain homogeneous initial data

global existence and decay properties for a degenerate keller segel model with a power factor in drift term abstract the following degenerate parabolic system modelling chemotaxis is considered ks u t u m u q 1 v x r n t 0 v t v v u x r n t 0 u x 0 u 0 x v x 0 v 0 x x r n where m 1 q 2 0 or 1 and n 1 the aim of this paper is to prove the existence of a time global weak solution u v of ks with the l 0 l r n bound such a global bound is obtained in the case of i m q 2 n for large initial data and ii 1 m q 2 n for small initial data in the case of ii the decay properties of the solution u v are also discussed

dirichlet heat kernel estimates for rotationally symmetric levy processes in this paper we consider a large class of purely discontinuous rotationally symmetric levy processes we establish sharp two sided estimates for the transition densities of such processes killed upon leaving an open set d w hend is a fat open set the sharp two sided estimates are given in terms of surviving probabilities and the global transition density of the levy process when d is a c 1 1 open set and the levy exponent of the process is given by 2 with being a complete bernstein function satisfying a mild growth condition at infinity our two sided estimates are explicit in terms of the distance function to the boundary of d and the levy density of x this gives an affirmative answer to the conjecture posted in chen kim and song global heat kernel estimates for relativistic stable processes in half space like open sets potential anal 36 2012 235 261 our results are the first sharp two sided dirichlet heat kernel estimates for a large class of symmetric levy processes with general levy exponents we also derive an explicit lower bound estimate for symmetric levy processes on r d in terms of their levy exponents

saddlepoint approximations for small sample logistic regression problems double saddlepoint approximations provide quick and accurate approximations to exact conditional tail probabilities in a variety of situations this paper describes the use of these approximations in two logistic regression problems an investigation of regression analysis of the log odds ratio in a sequence or set of 2 2 tables via simulation studies shows that in practical settings the saddlepoint methods closely approximate exact conditional inference the double saddlepoint approximation in the test for trend in a sequence of binomial random variates is also shown via simulation studies to be an effective approximation to exact conditional inference copyright 2000 john wiley sons ltd

strichartz type estimates for fractional heat equations abstract we obtain strichartz estimates for the fractional heat equations by using both the abstract strichartz estimates of keel tao and the hardy littlewood sobolev inequality we also prove an endpoint homogeneous strichartz estimate via replacing l x r n by bmo x r n and a parabolic homogeneous strichartz estimate meanwhile we generalize the strichartz estimates by replacing the lebesgue spaces with either besov spaces or sobolev spaces moreover we establish the strichartz estimates for the fractional heat equations with a time dependent potential of an appropriate integrability as an application we prove the global existence and uniqueness of regular solutions in spatial variables for the generalized navier stokes system with l r r n data

global existence and decay properties of solutions for some degenerate quasilinear parabolic systems modelling chemotaxis abstract the following degenerate parabolic system modelling chemotaxis is considered ks u t u m u v x r n t 0 v t v v u x r n t 0 u x 0 u 0 x v x 0 v 0 x x r n where 0 or 1 we show here that the system of ks with m 1 has a time global weak solution u v with a uniform bound in time when u 0 v 0 is a nonnegative function and in l 1 l r n l 1 h 1 w 1 r n u 0 m h 1 r n the decay properties of the solution with small initial data are also discussed

preventing blow up in a chemotaxis model abstract this paper deals with a chemotactic model of keller segel type the main feature of the keller segel model is the possibility of blow up of solutions in a finite time to eliminate the possibility of blow up a modified version of keller segel model is introduced the blow up control relies on the presence of a pressure function which increases faster than a logarithm for high enough cells densities for such a pressure function the solutions cannot blow up in a finite time some other conditions are introduced to ensure the global boundedness