numerical approximation for functionals of reflecting diffusion processes the aim of this paper is to approximate the expectation of a large class of functionals of the solution x xi of a stochastic differential equation with normal reflection in a piecewise smooth domain of rd this also yields a monte carlo method for solving partial differential problems of parabolic type with mixed boundary conditions the approximation is based on a modified euler scheme for the stochastic differential equation the scheme can be driven by a sequence of bounded independently and identically distributed i i d random variables or when the domain is convex by a sequence of gaussian i i d random variables the order of weak convergence for both cases is given in the former case the order of convergence is 1 2 and it is shown to be exact by an example in the last section numerical tests are presented the behavior of the error as a function of the final time t for fixed values of the discretization step and as a function of the discretization step for fixed values of the final

semidiscrete finite element approximations of a linear fluid structure interaction problem semidiscrete finite element approximations of a linear fluid structure interaction problem are studied first results concerning a divergence free weak formulation of the interaction problem are reviewed next semidiscrete finite element approximations are defined and the existence of finite element solutions is proved with the help of an auxiliary discretely divergence free formulation a discrete inf sup condition is verified and the existence of a finite element pressure is established strong a priori estimates for the finite element solutions are also derived then by passing to the limit in the finite element approximations the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained

estimators and tests in the analysis of multiple nonindependent 2 x 2 tables with partially missing observations we present methods for the analysis of a k variate binary measure for two independent groups where some observations may be incomplete as in the case of k repeated measures in a comparative trial for the k 2 x 2 tables let theta theta 1 theta k be a vector of association parameters where theta k is a measure of association that is a continuous function of the probabilities pi ik in each group i 1 2 k 1 k such as the log odds ratio or log relative risk the asymptotic distribution of the estimates theta theta 1 theta k is derived under the assumption that theta k theta for all k we describe the maximally efficient linear estimator theta of the common parameter theta tests of contrasts on the theta are presented which provide a test of homogeneity ha theta k theta l for all k not equal to l we then present maximally efficient tests of aggregate association hb theta theta 0 where theta 0 is a given value it is shown that the test of aggregate association hb is asymptotically independent of the preliminary test of homogeneity ha these methods generalize the efficient estimators of gart 1962 biometrics 18 601 610 and the cochran 1954 biometrics 10 417 451 mantel haenszel 1959 journal of the national cancer institute 22 719 748 and radhakrishna 1965 biometrics 21 86 98 tests to nonindependent tables the methods are illustrated with an analysis of repeated morphologic evaluations of liver biopsies obtained in the national cooperative gallstone study

a splitting step algorithm for reflected stochastic differential equations in r 1 a new algorithm which is based on the splitting step idea and the penalization method for reflected stochastic differential equation rsde in the upper half space r 1 is presented in this paper after some important estimates about rsdes and penalization odes are obtained the local pathwise error of the suggested algorithm are considered and an estimate of local error in the 2pth moment is proved under the assumptions of lipschitz continuity and linear growth some numerical experiments based on matlab programs are given to support the suggested algorithm

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

the use of maximin efficiency robust tests in combining contingency tables and survival analysis abstract a test is the maximin efficiency robust test for a family of possible models underlying the data if no other test has higher minimum efficiency relative to the asymptotically optimum test for each model methods used to examine the efficiency robustness of rank tests for the two sample problem are adapted to obtain maximin efficiency robust procedures for testing the equality of proportions across several 2 2 tables for combining the results of tests for trend in several 2 x j tables in which the dose response function is one of a set of possible monotone functions and to analyze censored survival data when either the wilcoxon or log rank may be appropriate in the survival setting the robust test has maximin efficiency 93 3 relative to the wilcoxon or long rank when each is optimum in contrast to the 75 relative efficiency each statistic has when the other is optimum

efficiency robust score tests for rodent tumourigenicity experiments summary the standard statistical test for assessing adverse effects in rodent tumourigenicity experiments is based on a time adjusted analysis of lethal and incidental tumours this test is shown to arise as the sum of two score statistics for fatal and incidental lesions respectively the former optimal against extreme value hazard alternatives and the latter optimal against logistic prevalence alternatives in terms of asymptotic relative efficiency in the pitman sense an efficiency robust test is developed which retains near full efficiency in the extreme value logistic situation as well as in other situations where the standard test may be only 70 efficient rodent tumourigenicity experiments are used to determine whether or not a particular agent results in an increase in tumour occurrence in animals exposed to this substance throughout their lifetimes as compared to unexposed controls the tumour status of an individual animal is normally determined at the time of death since many animals will die either from natural mortality or as a result of tumour development prior to the end of the study period information on tumourigenicity will accrue throughout the course of the experiment typically lasting about two years animals surviving to the end of the experiment are sacrificed and subjected to the same pathological evaluation as those dying prior to the termination time peto et al 1980 have proposed life table analysis of the lethal or fatal tumours and a prevalence analysis of the nonlethal or incidental tumours in the present paper we show that when the substance under study affects the occurrence of fatal and incidental lesions in a similar fashion their test can be formally derived as the sum of two score statistics for fatal and incidental tumours respectively the former statistic is the score test under extreme value hazard alternatives whereas the latter statistic is optimal against logistic prevalence alternatives because the true form of the underlying hazard and prevalence functions is unknown we develop in 3 an efficiency robust version of this test this is done by maximizing the minimum asymptotic relative efficiency within a finite class of hazard and prevalence functions applications of the maximin efficiency robust test are discussed in 4

finite element vibration analysis of fluid solid systems without spurious modes this paper deals with the finite element approximation of the vibration modes of a problem with fluid structure interaction displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation we introduce a nonconforming discretization error estimates for the approximation of eigenvalues and eigenvectors are given

rate of convergeance of a particle method for the solution of a 1d viscous scalar conservation law in a bounded interval in this paper we give a probabilistic interpretation of a viscous scalar conservation law in a bounded interval thanks to a nonlinear martingale problem the underlying nonlinear stochastic process is reflected at the boundary to take into account the dirichlet conditions after proving uniqueness for the martingale problem we show existence thanks to a propagation of chaos result indeed we exhibit a system of n interacting particles the empirical measure of which converges to the unique solution of the martingale problem as n as a consequence the solution of the viscous conservation law can be approximated thanks to a numerical algorithm based on the simulation of the particle system when this system is discretized in time thanks to the euler lepingle scheme d lepingle math comput simulation 38 1995 119 126 we show that the rate of convergence of the error is in o t 1 n where at denotes the time step finally we give numerical results which confirm this theoretical rate

an explicit formula for the skorokhod map on 0 a the skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions in this work an explicit formula for the skorokhod map 0 a on 0 a for any a 0 is derived specifically it is shown that on the space d 0 of right continuous functions with left limits taking values in r 0 a a o 0 where a d 0 d 0 is defined by a t t sups 0 t s a infu s t u and 0 d 0 d 0 is the skorokhod map on 0 which is given explicitly by 0 t t sup s 0 t s in addition properties of a are developed and comparison properties of 0 a are established

on the use of the generalized t and generalized rank sum statistics in medical research we have used monte carlo methods to compare the type i error properties of the conditional and unconditional versions of the generalized t and the generalized rank sum tests to those of the independent samples t and wilcoxon rank sum tests results showed inflated type i errors for the conditional generalized tests but not for the unconditional tests we also compared the power of the unconditional generalized tests to that of the t and wilcoxon tests under a variety of conditions results showed the generalized tests to be much more efficient than their traditional counterparts in some circumstances but substantially less powerful in others based on these and other considerations we conclude that the application of these newer statistics in medical research needs further consideration

traps for reflected brownian motion consider an open set d r d d 2 and a closed ball b d let e x tb denote the expectation of the hitting time of b for reflected brownian motion in d starting from x d we say that d is a trap domain if supx e x tb a domain d is not a trap domain if and only if the reflecting brownian motion in d is uniformly ergodic we fully characterize the simply connected planar trap domains using a geometric condition and give a number of less complete results for d 2

finite element analysis of compressible and incompressible fluid solid systems this paper deals with a finite element method to solve interior fluid structure vibration problems valid for compressible and incompressible fluids it is based on a displacement formulation for both the fluid and the solid the pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem lowest order triangular raviart thomas elements are used for the fluid and classical piece wise linear elements for the solid transmission conditions at the fluid solid interface are taken into account in a weak sense yielding a nonconforming discretization the method does not present spurious or circulation modes for nonzero frequencies convergence is proved and error estimates independent of the acoustic speed are given for incompressible fluids a convenient equivalent stream function formulation and a post process to compute the pressure are introduced

a posteriori error estimates in finite element acoustic analysis we present an a posteriori error estimator for the approximations of the acoustic vibration modes obtained by a finite element method which does not present spurious or circulation modes for non zero frequencies we prove that the proposed estimator is equivalent to the error in the approximation of the eigenvectors up to higher order terms with constants independent of the eigenvalues numerical results for some test examples are presented which show the good behavior of the estimator when it is used as local error indicator for adaptive refinement

finite element solution of incompressible fluid structure vibration problems in this paper we solve an eigenvalue problem arising from the computation of the vibrations of a coupled system incompressible fluid elastic structure in absence of external forces we use displacement variables for both the solid and the fluid but the fluid displacements are written as curls of a stream function classical linear triangular finite elements are used for the solid displacements and for the stream function in the fluid the kinematic transmission conditions at the fluid solid interface are taken into account in a weak sense by means of a lagrange multiplier the method does not present spurious or circulation modes for non zero frequencies numerical results are given for some test cases 1997 by john wiley sons ltd

probabilistic approach for nonlinear partial differential equations and stochastic partial differential equations with neumann boundary conditions abstract in this study we consider nonlinear partial differential equations pdes and stochastic pdes spdes with neumann boundary conditions on domains that satisfy the lions sznitmann saisho conditions using the convergence result based on the penalization approximation for stochastic differential equations with normal reflections on nonsmooth and nonconvex domains we establish the existence and comparison principle for the viscosity solutions of nonlinear pdes with the neumann conditions associated with the optimal control problem we also obtain for nonlinear spdes and backward spdes with neumann condition the representations of the stochastic viscosity solutions

on non parametric and generalized tests for the two sample problem with location and scale change alternatives various tests have been proposed for the two sample problem when the alternative is more general than a simple shift in location non parametric tests o brien s generalized t and rank sum tests and other tests related to the t we show that the generalized tests are directly related to non parametric tests proposed by lepage as a result we obtain a wider more flexible class of o brien type procedures which inherit the level robustness property of non parametric tests we have also computed the tests empirical sizes and powers under several models the non parametric procedures and the related o brien type tests are valid and yield good power in the settings investigated they are preferable to the t test and related procedures whose type i errors differ noticeably from nominal size for skewed and long tailed distributions

sweeping by a continuous prox regular set abstract the evolution problem known as sweeping process is considered for a class of nonconvex sets called prox regular or convex assuming essentially that such sets contain in the interior a suitable subset and move continuously w r t the hausdorff distance we prove local and global existence as well as uniqueness of solutions which are continuous functions with bounded variation some examples are presented

accurate pressure post process of a finite element method for elastoacoustics this paper deals with a post process to obtain a more accurate approximation of the fluid pressure from a finite element computation of the vibration modes of a fluid structure coupled system the underlying finite element method based on a displacement formulation for both media consists of using raviart thomas elements for the fluid combined with standard continuous elements for the solid an easy to compute post process of the pressure is derived the relation between this post process and an alternative finite element approximation of the problem based on discretizing the fluid pressure by enriched crouzeix raviart elements is studied higher order estimates for the l2 norm of the post processed pressure are proved by exploiting this relation as a by product higher order l2 estimates for the solid displacements obtained with the original method are also proved

on some impulse control problems with long run average cost some particular impulse control problems with infinite horizon and long run average cost are considered for markov processes having nice ergodicity properties the main feature of the method is to start with discounted cost and then let the discount factor go to zero this also gives an opportunity to study the asymptotic behavior of some optimal stopping time problems when the discount factor goes to zero probabilistic and analytical methods are used and examples are given especially for markov jump process and diffusion processes with reflection

modifying the t and anova f tests when treatment is expected to increase variability relative to controls summary when similar experimental units are assigned randomly to two groups one to receive a treatment the other to serve as a control the homogeneity of variance assumption underlying the pooled t test is valid under the null hypothesis of no treatment effect thus power and not validity of the pooled t should be the concern in such experiments especially if treatment may affect variability as well as mean response we focus on studies where there is a biological basis e g toxicological studies for expecting a treatment effect on mean response to be accompanied by an increase in variance to detect a change in mean response in such experimental situations we propose a simple modification of the pooled t that is also valid under ho no treatment effect but which can have substantially better power than the pooled t this modification can also be applied to other procedures for testing equality of means when there are two or more treatment groups in addition to the control

hamilton jacobi equations with state constraints in the present paper we consider hamilton jacobi equations of the form h x u vu 0 x e q where q is a bounded open subset of rn h is a given continuous real valued function of x s p e q x r x rn and vu is the gradient of the unknown function u we are interested in particular solutions of the above equation which are required to be supersolutions in a suitable weak sense of the same equation up to the boundary of q this requirement plays the role of a boundary condition the main motivation for this kind of solution comes from deterministic optimal control and differential games problems with constraints on the state of the system as well from related questions in constrained geodesics

a finite element solution of an added mass formulation for coupled fluid solid vibrations a finite element method to approximate the vibration modes of a structure in contact with an incompressible fluid is analyzed in this paper the effect of the fluid is taken into account by means of an added mass formulation which is one of the most usual procedures in engineering practice gravity waves on the free surface of the liquid are also considered in the model piecewise linear continuous elements are used to discretize the solid displacements the variables to compute the added mass terms and the vertical displacement of the free surface yielding a non conforming method for the spectral coupled problem error estimates are settled for approximate eigenfunctions and eigenfrequencies implementation issues are discussed and numerical experiments are reported in particular the method is compared with other numerical scheme based on a pure displacement formulation which has been recently analyzed

a stochastic differential game in the orthrant we study a zero sum stochastic differential game in the nonnegative orthrant the state of the system is governed by controlled reflecting diffusions in the nonnegative orthrant we consider discounted and average payoff evaluation criteria we prove the existence of values and optimal strategies for both payoff criteria

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

problemes de neumann quasilineaires on demontre l existence et l unicite de u c 2 r verifiant a id j x id ju x x du x dans u 0 sur udx 0 ou est un ouvert borne regulier a id j x est un champ de matrices definies positives regulier est une non linearite donnee est un champ de vecteurs regulier sur verifiant x n x 0 n etant la normale exterieure a

heavy traffic limits for the g h2 n m queue we establish heavy traffic stochastic process limits for queue length waiting time and overflow stochastic processes in a class ofg gi n m queueing models withn servers andm extra waiting spaces we let the arrival process be general only requiring that it satisfy a functional central limit theorem to capture the impact of the service time distribution beyond its mean within a markovian framework we consider a special class of service time distributions denoted byh2 which are mixtures of an exponential distribution with probabilityp and a unit point mass at 0 with probability 1 p these service time distributions exhibit relatively high variability having squared coefficients of variation greater than or equal to one as in halfin and whitt 1981 heavy traffic limits for queues with many exponential servers oper res 29 567 588 puhalskii and reiman 2000 the multiclassgi ph n queue in the halfin whitt regime adv appl probab 32 564 595 and garnett mandelbaum and reiman 2002 designing a call center with impatient customers manufacturing service oper management 4 208 227 we consider a sequence of queueing models indexed by the number of servers n and letn tend to infinity along with the traffic intensities nso that v n 1 n for 8 8 to treat finite waiting rooms we letm n v n for 0 8 with the specialh2 service time distribution the limit processes are one dimensional markov processes behaving like diffusion processes with different drift and diffusion functions in two different regions above and below zero we also establish a limit for theg m n m m model having exponential customer abandonments

weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatment summary in certain long term treatment trials one expects some lag period before the treatment is fully effective this paper presents two weighted log rank type statistics designed to have good efficiency over a wide range of lags a maximin efficiency robust statistic and a simplified version of this statistic both statistics can be computed as easily as the log rank statistic asymptotic efficiency calculations supported by small sample simulations show that the two proposed statistics are substantially more efficient than the conventional log rank statistic in certain lag situations with comparatively little efficiency loss relative to the log rank statistic when no lag exists we recommend the maximin statistic for situations where a lag is expected but cannot be specified precisely in advance

the order of convergence of eigenfrequencies in finite element approximations of fluid structure interaction problems in this paper we prove a double order for the convergence of eigenfrequencies in fluid structure vibration problems we improve estimates given recently for compressible and incompressible fluids to do this we extend classical results on finite element spectral approximation to nonconforming methods for noncompact operators

finite element approximation of spectral acoustic problems on curved domains this paper deals with the finite element approximation of the displacement formulation of the spectral acoustic problem on a curved non convex two dimensional domain convergence and error estimates are proved for raviart thomas elements on a discrete polygonal domain h inline equation in the framework of the abstract spectral approximation theory similar results have been previously proved only for polygonal domains numerical tests confirming the theoretical results are reported

comparing two samples extensions of the t rank sum and log rank tests abstract i consider the problem of testing that two populations are identical with respect to the distribution of a continuous variable against the alternative that values tend to be larger in one population i observe that the t rank sum and log rank tests are insensitive for a large class of alternatives that may be expected to occur commonly in practice propose a criterion for identifying this problem in a particular data set and propose corresponding extensions of the conventional methods the proposed methods should be useful for both identifying and interpreting group differences

continuous dependence results for non linear neumann type boundary value problems abstract we obtain estimates on the continuous dependence on the coefficient for second order non linear degenerate neumann type boundary value problems our results extend previous work of cockburn et al jakobsen and karlsen and gripenberg to problems with more general boundary conditions and domains a new feature here is that we account for the dependence on the boundary conditions as one application of our continuous dependence results we derive for the first time the rate of convergence for the vanishing viscosity method for such problems we also derive new explicit continuous dependence on the coefficients results for problems involving bellman isaacs equations and certain quasilinear equation

on the oblique derivative problem for diffusion processes and diffusion equations with holder continuous coefficients on a c2 domain in a euclidean space we consider the oblique derivative problem for a diffusion equation and assume the coefficients of the diffusion and boundary operators are holder continuous we then prove the uniqueness of diffusion processes and fundamental solutions corresponding to the problem for the purpose obtaining a stochastic representation of some so lutions to the problem plays a key role in our situation a difficulty arises from the absence of a fundamental solution with c2 smoothness up to the boundary it is overcome by showing some stability of a fundamental solution and a dif fusion process respectively under approximation of the domain in particular the stability of the fundamental solution is verified through construction it is done by applying the parametrix method twice to a parametrix with explicit expression

an efficiency robust nonparametric test for scale change for data from a gamma distribution when testing whether two samples came from a common distribution against the alternative that they differ in scale the asymptotically most powerful rank test depends on the density function underlying the data in some applications it is only known that the data are from a gamma distribution with increasing hazard rate i e the value of the shape parameter k is known to be 1 if the optimum test savage 1956 for data from an exponential law k 1 is used when the true value of k is much larger a loss of power or asymptotic relative efliciency results indeed the are of the exponential scores test relative to the optimum rank test for large k is about 81 4 this article presents the maximin efficiency robust test for the gamma k 1 family that has an asymptotic efficiency of at least 95 relative to the optimum test for each member of the family the test can be calculated using standard statistical packages and is illustrated on real data

the submartingale problem for a class of degenerate elliptic operators we consider the degenerate elliptic operator acting on c 2 b functions on 0 d mathcal l f x sum i 1 d a i x x i alpha i frac partial 2 f partial x i 2 x sum i 1 d b i x frac partial f partial x i x where the ai are continuous functions that are bounded above and below by positive constants the bi are bounded and measurable and the alpha i in 0 1 we impose neumann boundary conditions on the boundary of 0 d there will not be uniqueness for the submartingale problem corresponding to mathcal l if we consider however only those solutions to the submartingale problem for which the process spends 0 time on the boundary then existence and uniqueness for the submartingale problem for mathcal l holds within this class our result is equivalent to establishing weak uniqueness for the system of stochastic differential equations rm d x t i sqrt 2a i x t x t i alpha i 2 rm d w i t b i x t rm d t rm d l t x i quad x i t geq 0 where w t i are independent brownian motions and l x i t is a local time at 0 for xi

analysis of a finite element method for pressure potential formulation of elastoacoustic spectral problems a finite element method to approximate the vibration modes of a structure enclosing an acoustic fluid is analyzed the fluid is described by using simultaneously pressure and displacement potential variables whereas displacement variables are used for the solid a mathematical analysis of the continuous spectral problem is given the problem is discretized on a simplicial mesh by using piecewise constant elements for the pressure and continuous piecewise linear finite elements for the other fields error estimates are settled for approximate eigenvalues and eigenfrequencies finally implementation issues are discussed

finite element computation of the vibration modes of a fluid solid system abstract in this paper we solve the interior elastoacoustic problem by a finite element method which does not present spurious or circulation modes for nonzero frequencies it consists of classical triangular lagrangian elements for the solid and lowest order triangular raviart thomas elements for the fluid transmission conditions at the fluid solid interface are taken into account in a weak sense numerical results for some test examples are presented which show the good performance of the proposed methodology

powerful two sample tests based on the likelihood ratio a new approach to constructing nonparametric tests for the general two sample problem is proposed this approach not only generates traditional tests including the two sample kolmogorov smirnov cramer von mises and anderson darling tests but also produces new powerful tests based on the likelihood ratio although conventional two sample tests are sensitive to the difference in location most of them lack power to detect changes in scale and shape the new tests are location scale and shape sensitive so they are robust against variation in distribution

the effects of transformations and preliminary tests for non linearity in regression non linear relationships between two variables are often detected as a result of a preliminary statistical test for linearity common approaches to dealing with non linearity are to a make a linearizing transformation in the independent variable or b fit a relationship that is non linear in the independent variable such as including a quadratic term with either approach the resulting test for association between the two variables can have an inflated type i error we consider testing the significance of the quadratic term in a quadratic model as a preliminary test for non linearity using simulation experiments and asymptotic arguments we quantify the type i error inflation and suggest simple modifications of standard practice to protect the size of the type i error in the case of quadratic regression the type i error will be increased by roughly 50 per cent the simple strategy of appropriately correcting the alpha level is shown to have minimal loss of power if the relationship is truly linear in the case of a linearizing transformation the impact on the type i error will depend on the values of the independent variable and on the set of potential linearizing transformations considered simulation results suggest that a procedure which adjusts the test statistic according to the results of the preliminary test may offer adequate protection

a multidimensional process involving local time on presente une approche probabiliste a un probleme pose par mckean 1967 pour la construction d un systeme de n particules sur r avec un generateur formel

generalized bsdes and nonlinear neumann boundary value problems we study a new class of backward stochastic differential equations which involves the integral with respect to a continuous increasing process this allows us to give a probabilistic formula for solutions of semilinear partial differential equations with neumann boundary condition where the boundary condition itself is nonlinear we consider both parabolic and elliptic equations