a test of static equilibrium models and rates of return to quasi fixed factors with an application to the bell system abstract the paper provides a statistical test to assess the adequacy of the static equilibrium framework which can be used prior to specifying a fully dynamic equilibrium model we develop and apply this test to the production structure and factor demand equations based on the theory of restricted cost functions this diagnostic test can also be used in other areas of applied economics such as consumer demand and labor supply studies where the analyst faces the choice between static and dynamic models of economic behavior the framework is used to calculate rates of return to quasi fixed factors to measure the extent of over and underinvestment in such factors to adjust measured productivity growth for departures from static equilibrium and to provide measures of marginal tobin s q for individual assets that could be used to model investment functions for those assets

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

impulsive control in this paper the concept and principles of impulsive control are presented impulsive control can be applied to a class of systems whose state variables are changeable in a very short time period in particular the asymptotic stability of the impulsive control of a nonlinear system is given

mean square stability of analytic solution and euler maruyama method for impulsive stochastic differential equations from the view of algebra the mean square stability of analytic solutions and numerical solutions for impulsive stochastic differential equations are considered by the logarithmic norm the conditions under which the analytic and numerical solutions for a linear impulsive stochastic differential equation are mean square stable ms stable respectively are obtained the conditions are simple and easy to use some numerical experiments are given to illustrate the results

responses of strongly non linear oscillator parametrically excited by random narrow band noise the principal response of a strongly van der pol duffing oscillator subjected to parametric random narrow band excitation is investigated the technique of modified lindstedt poincare mlp method is used to transform the strongly non linear system to a weak one by introducing a new expansion parameter and then the multiple scales method is applied to determine the modulation equations for amplitude and phase of the response of the system the effect of damping detuning and bandwidth on the dynamic behaviors such as stability bifurcation are examined by computing the maximum lyapunov exponent analytically also the numerical simulation is carried out to verify the analytical results and random jump phenomenon may be observed in the region of the parameters of the system the excellent agreement between theoretical results and numerical ones can be found immediately and so the present method in this paper is applicable to solve strongly non linear problems

stability analysis of impulsive stochastic nonlinear systems this paper studies stochastic input to state stability and stochastic global stability for impulsive stochastic nonlinear systems using fixed dwell time condition and lyapunov based approach sufficient conditions are established for the stability properties two cases are studied 1 the case that the continuous dynamics is stable and 2 the case that the impulsive effects are stable furthermore the relations among different dwell time conditions are studied finally two examples are used to illustrate the developed theory

tests on the validity of static equilibrium models abstract this paper provides a framework to test the validity of static cost minimizing equilibrium assumptions that form the basis for much of the empirical literature on industrial production the point of departure in our model is to allow the observed technology to be at a short run equilibrium where firms minimize variable costs while being constrained by the utilization levels of quasi fixed factors the long run equilibrium is then inferred by minimizing total costs with the optimal adjustment of quasi fixed factor levels we use results from the optimization problem to form tests with respect to quantities and prices in the quantity space version departures between the actual and the optimal long run levels of quasi fixed factors are tested for statistical significance a significant non zero departure implies the rejection of a static equilibrium specification in the price space version the test is cast as a comparison of the market price and the long run shadow value of a quasi fixed factor although the two versions would give identical results in the non stochastic case the rejection powers of these two tests are found to depend on the particular functional form chosen to represent the production process i e cost function in an application based on aggregate u s manufacturing where capital is taken to be quasi fixed we were able to reject the static equilibrium specification these results cast doubt on the validity of a number of previous empirical studies

stability of impulsive functional differential equations abstract in this paper the stability of impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied by using lyapunov functions and razumikhin techniques some criteria of stability asymptotic stability and practical stability for impulsive functional differential equations in which the state variables on the impulses are related to the time delay are provided some examples are also presented to illustrate the efficiency of the results obtained

razumikhin type theorems on p th moment exponential stability of impulsive stochastic delay differential equations this note develops razumikhin type theorems on pth moment exponential stability for general impulsive stochastic delay differential equations some applications are also given to some special types of impulsive stochastic delay differential equations two examples illustrate the effectiveness of the proposed results

stability analysis for stochastic hybrid systems this survey addresses stability analysis for stochastic hybrid systems shs which are dynamical systems that combine continuous change and instantaneous change and that also include random effects we re emphasize the common features found in most of the models that have appeared in the literature which include stochastic switched systems markov jump systems impulsive stochastic systems switching diffusions stochastic impulsive systems driven by renewal processes diffusions driven by levy processes piecewise deterministic markov processes general stochastic hybrid systems and stochastic hybrid inclusions then we review many of the stability concepts that have been studied including lyapunov stability lagrange stability asymptotic stability and recurrence next we detail lyapunov based sufficient conditions for these properties and additional relaxations of lyapunov conditions many other aspects of stability theory for shs like converse lyapunov theorems and robustness theory are not fully developed hence we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces

the response envelope probability density function of a duffing oscillator with random narrow band excitation abstract a duffing oscillator excited by narrow band random noise can exhibit multi valued behaviour with random jumps between two pseudo stable states in this paper an approximate form of the probability density function or the envelope of the response is obtained state equations for the response envelope with the random excitation envelope as input are obtained by stochastic averaging the joint probability density function of response envelope and input envelope can be found approximately for certain ranges of the system parameters the response envelope probability density function shows two maxima in the cases where the response is multi valued numerical simulation confirms the results

stochastic averaging of strongly non linear oscillators under bounded noise excitation abstract a stochastic averaging method for strongly non linear oscillators under external and or parametric excitation of bounded noise is proposed by using the so called generalized harmonics functions the method is then applied to study the primary resonance of duffing oscillator with hardening spring under external excitation of bounded noise the stochastic jump and its bifurcation of the system are observed and explained by using the stationary probability density of amplitude and phase subsequently the method is applied to study the dynamical instability and parametric resonance of duffing oscillator with hardening spring under parametric excitation of bounded noise the primary unstable region is delineated by evaluating the lyapunov exponent of linearized system and the response and jump of non linear system around the unstable region are examined by using the sample functions and stationary probability density of amplitude and phase

exponential stability and instability of impulsive stochastic functional differential equations with markovian switching in this paper based on the lyapunov second method and razumikin techniques we establish some novel criteria on pth moment exponential stability almost exponential stability and instability of impulsive stochastic functional differential equations isfdes with markovian switching the findings show that impulsive stochastic functional equations with markovian switching can be exponentially stabilized by impulses finally an example is presented to illustrate the effectiveness and efficiency of the obtained results

multiple time scaling of the response of a duffing oscillator to narrow band random excitation the response of a duffing oscillator to narrow band random excitation is considered two approaches multiple time scaling and stochastic averaging are used both lead to the same set of three state equations for the slowly varying local mean square response or envelope and two other variables the stationary solution of these equations is similar to results previously obtained by using statistical linearization the stationary and nonstationary from the three state equations results compare favourably with digital simulations random jumps are shown to occur if the excitation bandwidth is sufficiently small

parametric tests for static and dynamic equilibrium econometric estimates of the characteristics of production are highly sensitive to the choice of dynamic specification in this paper we propose a new approach for testing whether inputs are in static equilibrium the procedure which is based on the use of a generalized cost function tests for divergences between the actual and static equilibrium quantities of all inputs simultaneously and symmetrically we apply it to two widely used data sets one at a high level of aggregation and the other at the firm level and strongly reject static equilibrium in both cases

exponential stability of euler maruyama solutions for impulsive stochastic differential equations with delay this paper establishes a method to study the exponential stability of euler maruyama em method for impulsive stochastic differential equations with delay by using the properties of m matrix and stochastic analysis technique some conditions under which the em solution is exponentially mean square stable are obtained some examples are provided to illustrate the results

mean square stability analysis of impulsive stochastic differential equations with delays in this article based on lyapunov krasovskii functional method and stochastic analysis theory we obtain some new criteria ensuring mean square stability of trivial solution of a class of impulsive stochastic differential equations with delays as an application a class of stochastic impulsive neural network with delays has been discussed one illustrative example has been provided to show the effectiveness of our results

some new criteria on p th moment stability of stochastic functional differential equations with markovian switching this note gives some new razumikhin type theorems on th moment stability of stochastic functional differential equations with markovian switching sfdewms by using auxiliary ordinary differential equation the main results of this note allow the diffusion operator associated with the underlying sfdewms of the lyapunov function along a solution of the system to be not always negative an example is provided to illustrate the effectiveness of the proposed results

short cuts to dynamic factor demand modelling abstract by means of so called virtual or shadow prices short run factor demands short run marginal costs etc can be derived from any long run cost function the traditional approach short run restricted conditional variable cost functions is criticized and it is also shown that technological change scale effects etc can be added to any cost function by means of disembodied factor augmenting efficiency indexes easing the interpretations of the effects but without loss of flexibility it is shown that the trend and scale parameters of the long run translog cost function can be directly translated into trend and scale parameters of such efficiency indexes the techniques are illustrated on the well known berndt wood data set using a diewert long run generalized leontief gl cost function and assuming that capital and labour are quasi fixed

stability of a random diffusion with linear drift we consider a linear system with markovian switching which is perturbed by gaussian type noise if the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable we also show that under certain conditions the linear system with markovian switching can be stabilized by such noisy perturbation

vector lyapunov function based input to state stability of stochastic impulsive switched time delay systems in this paper the input to state stability is studied for stochastic impulsive switched time delay systems using the vector lyapunov function average dwell time and the properties of m matrix different types of sufficient conditions are established both the case that the continuous dynamics is stable and the case that the discrete dynamics is stable are addressed and the stability conditions are obtained in the obtained stability conditions different components of the vector lyapunov function are allowed to be coupled the information in consecutive impulsive switching intervals is also allowed to be coupled therefore the magnification on the corresponding coupling items is avoided and the obtained results are more general and less conservative than the existing results furthermore we investigate the relationships among the vector lyapunov function approach the approach based on the comparison principle and the scalar lyapunov function approach according to the vector lyapunov function the comparison system is constructed and the scalar lyapunov function based stability conditions are established finally the applicability of our results is illustrated through two examples from neural systems and the synchronization problem of chaos based secure communication systems

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

finite time stability of linear time varying singular systems with impulsive effects in this paper we introduce a new concept of finite time stability of linear time varying singular systems with impulses at fixed times and present new results for the above mentioned class of system in the form of sufficient conditions a sufficient condition is given in terms of matrix inequalities which gives the opportunity of fitting the finite time control problem in the general framework via impulsive control a numerical example is presented to illustrate the efficiency of the proposed result

exponential stability of stochastic differential delay systems with delayed impulse effects in this paper we investigate the stability of stochastic delay differential systems with delayed impulses by razumikhin methods some criteria on the pth moment exponential stability are obtained it is shown that if a stochastic delay differential system is exponentially stable then under some conditions its stability is robust or weaken with respect to delayed impulses moreover it is also shown that an unstable stochastic delay system can be successfully stabilized by delayed impulses the effectiveness of the proposed results is illustrated by three examples

p moment stability of stochastic differential equations with jumps in the paper p moment stability of stochastic differential equations with jumps is considered first some preliminary notes are given then several theorems on p moment stability of these equations are established using liapunov function at last an example is present to show application of the obtained results

construction of strict lyapunov krasovskii functionals for time varying time delay systems abstract for stability analysis of time varying time delay systems it is known that time derivatives time shifts in the discrete time setting of the lyapunov krasovskii functionals lkfs for both internal stability and input to state stability iss can be indefinite which can improve the resulting stability conditions in some cases however the non strict lkfs may be insufficient and inconvenient to use in practice in this paper based on the non strict iss lkfs for time varying time delay systems and with the help of uniformly asymptotically stable uas and uniformly exponentially bounded ueb scalar functions three classes of strict iss lkfs are constructed such that their time derivatives are strictly negative definite along the trajectories of the considered system a general construction of strict iss lkfs by using the positive definite and uniformly bounded solution to a scalar lyapunov differential equation is established which includes the proposed three classes of strict iss lkfs as special cases the approaches are also extended to deal with a lyapunov inequality whose right hand side is indefinite and nonlinear both continuous time and discrete time systems are considered the effectiveness of the proposed methods is illustrated by some examples borrowed from the literature

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

moment exponential stability of stochastic delay systems with delayed impulse effects at random times and applications in the stabilisation of stochastic neural networks in this paper we investigate the exponential stability for a class of impulsive stochastic functional differential equations with delayed impulse effects the impulse instants considered in this p

improved razumikhin and krasovskii stability criteria for time varying stochastic time delay systems the problem of pth moment stability for time varying stochastic time delay systems with markovian switching is investigated in this paper some novel stability criteria are obtained by applying the generalized razumikhin and krasovskii stability approaches both pth moment asymptotic stability and integral input to state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison lemmas the established results show that time derivatives of the constructed razumikhin functions and krasovskii functionals are allowed to be indefinite which improve the existing results on this topic by applying the obtained results for stochastic systems we also analyze briefly the stability of time varying deterministic time delay systems finally examples are provided to illustrate the effectiveness of the proposed results

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

ex post tests for short and long run optimization abstract the purpose of this paper is to develop tests of long run equilibrium models where the long run is defined as the state where the observed levels of output and capital are consistent with optimizing behavior we use the implied relationship between a restricted translog cost function and derived demand equations to provide a series of nested tests which can be interpreted as ex post tests for short and long run optimization behavior a set of parameter restrictions on the translog system are specified for testing whether observable levels of capital and or output of a firm correspond to the long run optimal level our tests of the validity of long run equilibrium specifications are based on data for 28 german industries for the period 1960 1981 for most of the industries the set of restrictions implied by long run equilibrium had to be rejected

brief continuous time state feedback h2 control of markovian jump linear systems via convex analysis continuous time h 2 control problem for the class of linear systems with markovian jumps mjls using convex analysis is considered in this paper the definition of the h 2 norm for continuous time mjls is presented and related to the appropriate observability and controllability gramians a convex programming formulation for the h 2 control problem of mjls is developed that enables us to tackle the optimization problem of mjls under the assumption that the transition rate matrix p p i j for the markov chain may not be exactly known but belongs to an appropriate convex set an equivalence between the convex formulation when p is exactly known and the usual dynamic programming approach of quadratic optimal control of mjls is established it is shown that there exists a solution for the convex programming problem if and only if there exists the mean square stabilizing solution for a set of coupled algebraic riccati equations these results are compared with other related works in the current literature

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product

stability of square mean almost automorphic mild solutions to impulsive stochastic differential equations driven by g brownian motion in this paper we consider a class of impulsive stochastic differential equations driven by g brownian motion igsdes in short in particular we study the exponentially and quasi sure exponentia