asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

the sr approach a new estimation procedure for non linear and non gaussian dynamic term structure models abstract this paper suggests a new approach for estimating linear and non linear dynamic term structure models with latent factors we impose no distributional assumptions on the factors which therefore may be non gaussian the novelty of our approach is to use many observables yields or bond prices in the cross section dimension this implies that the latent factors can be determined quite accurately by a sequence of cross section regressions we also show how output from these regressions can be used to obtain model parameters by a two or three step moment based estimation procedure

asymptotically periodic solutions of n competing species problem with time delays abstract a general nonautonomous lotka volterra system of integro differential equations with infinite delay is considered and sufficient conditions for uniform stability and asymptotic stability of solutions are investigated these limiting equations are used to obtain the existence of asymptotically periodic solutions of the corresponding system of equations where lower limit in the integration is zero

hac estimation in a spatial framework abstract we suggest a non parametric heteroscedasticity and autocorrelation consistent hac estimator of the variance covariance vc matrix for a vector of sample moments within a spatial context we demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial models we allow for more than one measure of distance each of which may be measured with error monte carlo results suggest that our estimator is reasonable in finite samples we then consider a spatial model containing various complexities and demonstrate that our hac estimator can be applied in the context of that model

a multidimensional stochastic singular control problem via dynkin game and dirichlet form the traditional difficulty with stochastic singular control is characterizing the regularities of the value function and the optimal control policy in this paper a multidimensional singular control problem is considered we found the optimal value function and the optimal control policy of this problem via a dynkin game whose solution is given by the saddle point of the cost function the existence and uniqueness of the solution to this dynkin game are proved through an associated variational inequality problem involving dirichlet form as a consequence the properties of the value function of this dynkin game imply the smoothness of the value function of the stochastic singular control problem in this way we are able to show the existence of a classical solution to this multidimensional singular control problem which was traditionally solved in the sense of viscosity solutions and this enables the application of the verification theorem to prove optimality

existence uniqueness and global asymptotic stability of positive solutions of a predator prey system with holling ii functional response with random perturbation abstract this paper discusses a randomized two species predator prey system with holling ii functional response we show that the positive solution of the associated stochastic delay differential equation does not explode to infinity in a finite time in addition the existence uniqueness and global asymptotic stability of the positive solutions are studied

competitive lotka volterra population dynamics with jumps abstract this paper considers competitive lotka volterra population dynamics with jumps the contributions of this paper are as follows a we show that a stochastic differential equation sde with jumps associated with the model has a unique global positive solution b we discuss the uniform boundedness of the p th moment with p 0 and reveal the sample lyapunov exponents c using a variation of constants formula for a class of sdes with jumps we provide an explicit solution for one dimensional competitive lotka volterra population dynamics with jumps and investigate the sample lyapunov exponent for each component and the extinction of our n dimensional model

stochastic persistence and stationary distribution in a holling tanner type prey predator model abstract in this paper we study a stochastic predator prey model with beddington deangelis type functional response and logistic growth for predators the deterministic model is already well studied and we recall some important results here we construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations for the stochastic model we show that the system admits unique positive global solution starting from the positive initial value then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes finally we show that the system has a stationary distribution under certain parametric restrictions numerical simulations are carried out to substantiate the analytical results

minimizing infinite time horizon discounted cost with mean variance and bounded variation controls we consider an infinite time horizon discounted cost minimization problem for a class of ito processes the available controls are drift and diffusion coefficients and the added bounded variation process we show that the value function is twice continuously differentiable and derive an optimal policy which has feedback type drift and diffusion coefficients when the absolute value of the optimal drift grows faster than the running cost function the optimal bounded variation process is identically zero when it grows weaker than the running cost function optimal bounded variation process is a local time type process in this case we relate the control problem with an optimal stopping problem we also establish the abelian limit relations between the value functions of the discounted cost problem and the stationary problem

spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix this paper considers spatial heteroskedasticity and autocorrelation consistent spatial hac estimation of covariance matrices of parameter estimators we generalize the spatial hac estimator introduced by kelejian and prucha 2007 to apply to linear and nonlinear spatial models with moment conditions we establish its consistency rate of convergence and asymptotic truncated mean squared error mse based on the asymptotic truncated mse criterion we derive the optimal bandwidth parameter and suggest its data dependent estimation procedure using a parametric plug in method the finite sample performances of the spatial hac estimator are evaluated via monte carlo simulation

stochastic functional kolmogorov type population dynamics abstract in this paper we stochastically perturb the functional kolmogorov type system x t diag x 1 t x n t f x t into the stochastic functional differential equation d x t diag x 1 t x n t f x t d t g x t d w t this paper studies existence and uniqueness of the global positive solution and its asymptotic bound properties and moment average in time these properties are natural requirements from the biological point of view as the special cases we discuss the various stochastic lotka volterra systems

inference on difference in differences average treatment effects a fixed b approach abstract this paper provides an analysis of the standard errors proposed by driscoll and kraay 1998 dk in linear difference in differences dd models with fixed effects and individual specific time trends the analysis is accomplished within the fixed b asymptotic framework developed by kiefer and vogelsang 2005 for heteroskedasticity and autocorrelation consistent hac covariance matrix estimator based tests for both the fixed n large t and large n large t cases it is shown that fixed b asymptotic distributions of test statistics constructed using the dd estimator and the dk standard errors are different from the results found by kiefer and vogelsang 2005 and vogelsang 2012 the newly derived fixed b asymptotic distributions depend on the date of policy change individual specific trend functions as well as the choice of kernel and bandwidth monte carlo simulations illustrate the performance of the fixed b approximations in practice

critical behavior of propagation on small world networks we report numerical evidence that an epidemiclike model which can be interpreted as the propagation of a rumor exhibits critical behavior at a finite randomness of the underlying small world network the transition occurs between a regime where the rumor dies in a small neighborhood of its origin and a regime where it spreads over a finite fraction of the whole population critical exponents are evaluated through finite size scaling analysis and the dependence of the critical randomness with the network connectivity is studied the behavior of this system as a function of the small network randomness bears noticeable similarities with an epidemiological model reported recently m kuperman and g abramson phys rev lett 86 2909 2001 in spite of substantial differences in the respective dynamical rules

a bounded variation control problem for diffusion processes we consider an infinite horizon discounted cost minimization problem for a one dimensional stochastic differential equation model the available control is an added bounded variation process the cost structure involves a running cost function and a proportional cost for the use of the control process the running cost function is not necessarily convex we obtain sufficient conditions to guarantee the optimality of the zero control also for unbounded cost functions we provide sufficient conditions which make our optimal state process a reflecting diffusion on a compact interval in both cases the value function is a c2 function for bounded cost functions under additional assumptions we obtain a complex optimal strategy which turned out to be a mixture of jumps and local time type processes in this case we show that the value function is only a c1 function and that it fails to be a c2 function we also discuss a related variance control problem

persistence attractivity and delay in facultative mutualism abstract relations between persistence and ultimate boundedness of the solutions of the lotka volterra system dx t dt x t r 1 a 11 x t a 22 y t dy t dt y t r 2 a 21 x t a 22 y t modelling facultative mutualism with delayed responses are established and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay system

stationary distribution and extinction of a stochastic seir epidemic model with standard incidence abstract in this paper we consider a stochastic seir epidemic model with standard incidence by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of ergodic stationary distribution to the model our result does not depend on the positive endemic equilibrium e of the deterministic system which improves the previous result to a greater extent moreover we also establish sufficient conditions for extinction of the disease

effects of time delay on symmetric two species competition subject to noise noise and time delay act simultaneously on real ecological systems the lotka volterra model of symmetric two species competition with noise and time delay was investigated in this paper by means of stochastic simulation we find that i the time delay induces the densities of the two species to periodically oscillate synchronously ii the stationary probability distribution function of the two species densities exhibits a transition from multiple to single stability as the delay time increases iii the characteristic correlation time for the sum of the two species densities squared exhibits a nonmonotonic behavior as a function of delay time our results have the implication that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems

spatial correlation robust inference with errors in location or distance this paper presents results from a monte carlo study concerning inference with spatially dependent data we investigate the impact of location distance measurement errors upon the accuracy of parametric and nonparametric estimators of asymptotic variances nonparametric estimators are quite robust to such errors method of moments estimators perform surprisingly well and mle estimators are very poor we also present and evaluate a specification test based on a parametric bootstrap that has good power properties for the types of measurement error we consider

a likelihood ratio test for spatial model selection abstract this paper develops a nondegenerate likelihood ratio test for model selection between two competitive spatial econometrics models it generalizes the test of vuong 1989 to models with spatial near epoch dependent ned data we do not make any structural assumption on the true model specification and allow for the cases where both or one of the two competing models are mis specified the test is valid whether two models are nested or non nested as a prerequisite of the test we first show that quasi maximum likelihood estimators qmle of spatial econometrics models are consistent estimators of their pseudo true values and are asymptotically normal under regularity conditions in particular we study spatial autoregressive models with spatial autoregressive errors sarar and matrix exponential spatial specification mess models we derive the limiting null distribution of the test statistic a spatial heteroskedastic and autoregressive consistent estimator of asymptotic variance of the test statistic under the null which is necessary to implement the test is constructed monte carlo experiments are designed to investigate finite sample performance of qmles for sarar and mess models as well as the size and power of the proposed test

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

an abelian limit approach to a singular ergodic control problem we consider an ergodic stochastic control problem for a class of one dimensional ito processes where the available control is an added bounded variation process the corresponding infinite horizon discounted control problem was solved in a weerasinghe siam j control optim 44 2005 pp 389 417 here we show that as the discount factor approaches zero the optimal strategies derived in a weerasinghe siam j control optim 44 2005 pp 389 417 converge to an optimal strategy for the ergodic control problem under different assumptions two types of optimal strategies were derived also the abelian limit relationships among the ergodic control problem the infinite horizon discounted control problem and the finite time horizon control problem are established here a solution to a constrained optimization problem is obtained as an application

asymptotic behavior of stochastic multi group epidemic models with distributed delays abstract in this paper we introduce stochasticity into multi group epidemic models with distributed delays and general kernel functions the stochasticity in the model is a standard technique in stochastic population modeling when the perturbations are small by using the method of stochastic lyapunov functions we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number r 0 if r 0 1 the solution of the stochastic system oscillates around the disease free equilibrium e 0 while if r 0 1 the solution of the stochastic model fluctuates around the endemic equilibrium e moreover we also establish sufficient conditions of these results

singular optimal controls of stochastic recursive systems and hamilton jacobi bellman inequality abstract in this paper we study the optimal singular controls for stochastic recursive systems in which the control has two components the regular control and the singular control under certain assumptions we establish the dynamic programming principle for this kind of optimal singular controls problem and prove that the value function is a unique viscosity solution of the corresponding hamilton jacobi bellman inequality in a given class of bounded and continuous functions at last an example is given for illustration

heteroskedasticity autocorrelation and spatial correlation robust inference in linear panel models with fixed effects abstract this paper develops an asymptotic theory for test statistics in linear panel models that are robust to heteroskedasticity autocorrelation and or spatial correlation two classes of standard errors are analyzed both are based on nonparametric heteroskedasticity autocorrelation hac covariance matrix estimators the first class is based on averages of hac estimators across individuals in the cross section i e averages of hacs this class includes the well known cluster standard errors analyzed by arellano 1987 as a special case the second class is based on the hac of cross section averages and was proposed by driscoll and kraay 1998 the hac of averages standard errors are robust to heteroskedasticity serial correlation and spatial correlation but weak dependence in the time dimension is required the averages of hacs standard errors are robust to heteroskedasticity and serial correlation including the nonstationary case but they are not valid in the presence of spatial correlation the main contribution of the paper is to develop a fixed b asymptotic theory for statistics based on both classes of standard errors in models with individual and possibly time fixed effects dummy variables the asymptotics is carried out for large time sample sizes for both fixed and large cross section sample sizes extensive simulations show that the fixed b approximation is usually much better than the traditional normal or chi square approximation especially for the driscoll kraay standard errors the use of fixed b critical values will lead to more reliable inference in practice especially for tests of joint hypotheses

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

on the principle of smooth fit for a class of singular stochastic control problems for diffusions this paper considers the principle of smooth fit for a class of one dimensional singular stochastic control problems allowing the system to be of nonlinear diffusion type the existence and the uniqueness of a convex c 2 solution to the corresponding variational inequality are obtained it is proved that this solution gives the value function of the control problem and the optimal control process is constructed as an example of the degenerate case it is proved that the conclusion is also true for linear systems and the explicit formula for the smooth fit points is derived

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

the cross quantilogram measuring quantile dependence and testing directional predictability between time series this paper proposes the cross quantilogram to measure the quantile dependence between two time series we apply it to test the hypothesis that one time series has no directional predictability to another time series we establish the asymptotic distribution of the cross quantilogram and the corresponding test statistic the limiting distributions depend on nuisance parameters to construct consistent confidence intervals we employ the stationary bootstrap procedure we show the consistency of this bootstrap also we consider the self normalized approach which is shown to be asymptotically pivotal under the null hypothesis of no predictability we provide simulation studies and two empirical applications first we use the cross quantilogram to detect predictability from stock variance to excess stock return compared to existing tools used in the literature of stock return predictability our method provides a more complete relationship between a predictor and stock return second we investigate the systemic risk of individual financial institutions such as jp morgan chase goldman sachs and aig this article has supplementary materials online

a stage structured predator prey model of beddington deangelis type we formulate and study a robust stage structured predator prey model of beddington deangelis type functional response the time delay is the time taken from birth to maturity the beddington deangelis functional response is similar to the holling type 2 functional response but contains an extra term describing mutual interference by predators first we show that the predator coexists with prey permanently if and only if the predator s recruitment rate at the peak of prey abundance is larger than its death rate second we show that if the system is permanent then a sufficiently large degree of the predator interference can not only stabilize the system but also guarantee the stability of the system against the increase of the carrying capacity of prey and the increase of birth rate of the adult predator third we show both analytically and numerically that stability switches of interior equilibrium may occur as maturation time delay increases stability may change from stable to unstable to finally stable implying that a large delay can be stabilizing

optimal bandwidth selection in heteroskedasticity autocorrelation robust testing the paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors the studentization is based on robust standard errors with truncation lag m bt for some constant b 2 0 1 and sample size t it is shown that the nonstandard xed b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the nite sample distributions than the standard small b limit distribution we further show that for typical economic time series the optimal bandwidth that minimizes a weighted average of type i and type ii errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long run variance estimator a plug in procedure for implementing this optimal bandwidth is suggested and simulations not reported here con rm that the new plug in procedure works well in nite samples

analysis of autonomous lotka volterra competition systems with random perturbation abstract this paper discusses a randomized n species lotka volterra competition system we show that this system is stable in time average under certain conditions furthermore there is a stationary distribution of this system if extra conditions are satisfied also we give the extinction condition of this system finally numerical simulations are carried out to support our results

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects abstract this paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms we propose a bivariate kernel covariance estimator that nests existing estimators as special cases our estimator improves upon existing estimators in terms of robustness efficiency and adaptiveness for distributional approximations we considered two types of asymptotics the increasing smoothing asymptotics and the fixed smoothing asymptotics under the former asymptotics the wald statistic based on our covariance estimator converges to a chi square distribution under the latter asymptotics the wald statistic is asymptotically equivalent to a distribution that can be well approximated by an f distribution simulation results show that our proposed testing procedure works well in finite samples

stochastic permanence of an siqs epidemic model with saturated incidence and independent random perturbations abstract this article discusses a stochastic siqs epidemic model with saturated incidence we assume that random perturbations always fluctuate at the endemic equilibrium the existence of a global positive solution is obtained by constructing a suitable lyapunov function under some suitable conditions we derive the stochastic boundedness and stochastic permanence of the solutions of a stochastic siqs model some numerical simulations are carried out to check our results

exponential extinction of a stochastic predator prey model with allee effect abstract in this paper we study a stochastic predator prey model with beddington deangelis functional response and allee effect whose coefficients are dependent on expectations we prove that there is a unique global positive solution to the system with the positive initial value moreover sufficient conditions for exponential extinction are established

stochastic delay lotka volterra model we reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay lotka volterra model but will also make the solutions to be stochastically ultimately bounded to reveal these interesting facts we stochastically perturb the delay lotka volterra model x t diag x1 t xn t b ax t into the ito form dx t diag x1 t xn t b ax t dt x t dw t and show that although the solution to the original delay equation may explode to infinity in a finite time with probability one that of the associated stochastic delay equation does not we also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix a

three limit cycles in a leslie gower predator prey model with additive allee effect in this work a bidimensional continuous time differential equations system is analyzed which is derived of leslie type predator prey schemes by considering a nonmonotonic functional response and allee effect on population prey for the system obtained we describe the bifurcation diagram of limit cycles that appears in the first quadrant the only quadrant of interest for the sake of realism we show that under certain conditions over the parameters the system allows the existence of three limit cycles the first two cycles are infinitesimal ones generated by hopf bifurcation the third one arises from a homoclinic bifurcation furthermore we give conditions over the parameters such that the model allows long term extinction or survival of both populations in particular the presence of a weak allee effect does not imply extinction of populations necessarily for our model

singular control of stochastic linear systems with recursive utility we formulate a class of singular stochastic control problem with recursive utility where the cost function is determined by a backward stochastic differential equation some characteristics of the value function of the control problem are obtained by the method of approximation via penalization and the optimal control process is constructed

a note on a stage specific predator prey stochastic model abstract in this work we analyze a modified version of a stage specific structure in a predator prey model recently introduced in the literature we assume that the predator death rate is subject to randomness and we discuss through both a theoretical and a computational approach about the influence of this assumption in the behavior of the process

asymptotic behavior of a stochastic delayed seir epidemic model with nonlinear incidence abstract this paper is concerned with a stochastic delayed seir epidemic model with nonlinear incidence firstly we verify that there exists a unique global positive solution of the system then by constructing some suitable lyapunov functions we study the asymptotic behaviors of the disease free equilibrium and the endemic equilibrium respectively

dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size abstract in this paper we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system

a class of singular control problems and the smooth fit principle this paper analyzes a class of singular control problems for which value functions are not necessarily smooth necessary and sufficient conditions for the well known smooth fit principle along with the regularity of the value functions are given explicit solutions for the optimal policy and for the value functions are provided in particular when payoff functions satisfy the usual inada conditions the boundaries between action and continuation regions are smooth and strictly monotonic as postulated and exploited in the existing literature see a k dixit and r s pindyck investment under uncertainty princeton university press princeton nj 1994 m h a davis et al adv in appl probab 19 1987 pp 156 176 t o kobila stochastics stochastics rep 43 1993 pp 29 63 a b abel and j c eberly j econom dynam control 21 1997 pp 831 852 a oksendal finance stoch 4 2000 pp 223 250 j a scheinkman and t zariphopoulou j econom theory 96 2001 pp 180 207 a merhi and m zervos siam j control optim 46 2007 pp 839 876 and l h alvarez a general theory of optimal capacity accumulation under price uncertainty and costly reversibility working paper helsinki center of economic research helsinski finland 2006 illustrative examples for both smooth and nonsmooth cases are discussed to emphasize the pitfall of solving singular control problems with a priori smoothness assumptions

gmm estimation with cross sectional dependence this paper presents a spatial model of dependence among agents using a metric of economic distance measurements of this economic distance provide cross sectional data with a structure similar to that provided by the time index in time series data generalized method of moments estimators using such dependent data are shown to be consistent and asymptotically normal this paper presents a class of non parametric positive semi definite covariance matrix estimators that allow for general forms of dependence characterized by economic distance these covariance matrix estimators are shown to remain consistent when economic distances are not precisely observed

autoregressive spatial spectral estimates abstract nonparametric spectral density estimates find many uses in econometrics for stationary random fields on a regular spatial lattice we propose an autoregressive nonparametric spectral density estimate that is guaranteed positive even when suitable edge effect correction is employed and is simple to compute using least squares our estimate is based on truncating a true half plane infinite autoregressive representation while also allowing the truncation length to diverge in all dimensions to avoid the potential bias due to truncation at a fixed lag length uniform consistency of the proposed estimate is established and new criteria for order selection are also suggested and studied in practical settings the asymptotic distribution of the estimate is shown to be zero mean normal and independent at fixed distinct frequencies mirroring the behaviour for time series a small monte carlo experiment examines finite sample performance technically the key to the results is the covariance structure of stationary random fields defined on regularly spaced lattices we show the covariance matrix to satisfy a generalization of the toeplitz property familiar from time series analysis

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

impulse control of multidimensional jump diffusions this paper studies regularity properties of the value function for an infinite horizon discounted cost impulse control problem where the underlying controlled process is a multidimensional jump diffusion with possibly infinite activity jumps surprisingly despite these jumps we obtain the same degree of regularity as for the diffusion case at least when the jump satisfies certain integrability conditions

some new results of nonautonomous lotka volterra competitive systems with delays abstract in this paper we improve and generalize the results of montes de oca and zeeman j math anal appl 192 1995 360 370 proc amer math soc 124 1996 3677 3687 to general n species nonautonomous lotka volterra type competitive systems with finite or infinite delays we establish a series of criteria under which a part of the n species of the systems is driven to extinction while the remaining part of the n species is persistent or uniformly persistent or coexists globally asymptotically stable