root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

perturbation of symmetric markov processes we present a path space integral representation of the semigroup associated with the quadratic form obtained by a lower order perturbation of the l 2 infinitesimal generator mathcal l of a general symmetric markov process an illuminating concrete example for mathcal l is delta d delta s d where d is a bounded euclidean domain in mathbb r d s in 0 1 delta d is the laplace operator in d with zero dirichlet boundary condition and delta s d is the fractional laplacian in d with zero exterior condition the strong markov process corresponding to mathcal l is a levy process that is the sum of brownian motion in mathbb r d and an independent symmetric 2s stable process in mathbb r d killed upon exiting the domain d this probabilistic representation is a combination of feynman kac and girsanov formulas crucial to the development is the use of an extension of nakao s stochastic integral for zero energy additive functionals and the associated ito formula both of which were recently developed in chen et al stochastic calculus for dirichlet processes preprint 2006

stabilization of the inverted linearized pendulum by high frequency vibrations in this note we give a simple geometrical picture that explains why an inverted pendulum is stabilized by high frequency vibrations

geometrical aspects of stability theory for hill s equations where a and b are real parameters apparently the first stability diagram was drawn in the classical paper by b van der pol m j o sti utt 15 since then many papers and textbooks have appeared on the subject we mention j j stoker 13 j meixner f w sch fke 12 d m levy 8 j b keller 11 m i weinstein j b keller 16 17 j poschel e trubowltz 9 and v i arnold 3 5 6 this literature contains extensive estimates on the order of tangency of resonance tongues and the behavior of stability boundaries at infinity a full understanding of the stability diagrams is still lacking for instance the appearance of instability pockets in some cases see figure 1 cf 15 calls for a geometric explanation it should be noted that this phenomenon does not occur in the classical mathieu case cf 12 for a preliminary study near resonances using singularity theory we refer to afsharnejad 1 related bifurcational aspects of nonlinear perturbations of mathieu s equation near resonances were studied by broer vegter 7 the global geometry of the symplectic group was used for a stability proof of a hill equation in levi 10 we introduce the main object of study of this paper

stability of the inverted pendulum a topological explanation an explanation and a proof of stability of the inverted pendulum whose suspension point undergoes vertical periodic oscillations is given the main idea of the argument is topological as it turns out existence of stable regimes can be proven with little effort using only very crude qualitative information about the system more precisely let n be the number of times the pendulum becomes vertical during one forcing period if n changes by more than 4 with the change of a parameter mu then for an open interval of intermediate values of mu the pendulum will be stable

a reversible bifurcation analysis of the inverted pendulum the inverted pendulum with a periodic parametric forcing is considered as a bifurcation problem in the reversible setting parameters are given by the size of the forcing and the frequency ratio normal form theory provides an integrable approximation of the poincare map generated by a planar vector field genericity of the model is studied by a perturbation analysis where the spatial symmetry is optional here equivariant singularity theory is used

semiparametric analysis of random effects linear models from binary panel data andersen 1970 considered the problem of inference on random effects linear models from binary response panel data he showed that inference is possible if the disturbances for each panel member are known to be white noise with the logistic distribution and if the observed explanatory variables vary over time a conditional maximum likelihood estimator consistently estimates the model parameters up to scale the present paper shows that inference remains possible if the disturbances for each panel member are known only to be time stationary with unbounded support and if the explanatory variables vary enough over time a conditional version of the maximum score estimator manski 1975 1985 consistently estimates the model parameters up to scale

on the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum abstract by the use of interval methods it is proven that there exists an unstable periodic solution to the damped and periodically forced pendulum around the upper equilibrium it is also proved that this solution can be stabilized by a control which does not need the knowledge of values of the state variables but of the unstable periodic solution

degenerate lower dimensional tori in reversible systems abstract in this paper we prove the persistence of lower dimensional invariant tori with prescribed frequencies and singular normal matrices in reversible systems the normal variable is two dimensional and the unperturbed nonlinear terms in the differential equation for this variable have a special structure

umbilical torus bifurcations in hamiltonian systems we consider perturbations of integrable hamiltonian systems in the neighbourhood of normally umbilic invariant tori these lower dimensional tori do not satisfy the usual non degeneracy conditions that would yield persistence by an adaption of kam theory and there are indeed regions in parameter space with no surviving torus we assume appropriate transversality conditions to hold so that the tori in the unperturbed system bifurcate according to a generalised umbilical catastrophe combining techniques of kam theory and singularity theory we show that such bifurcation scenarios of invariant tori survive the perturbation on large cantor sets applications to gyrostat dynamics are pointed out

extremal values of smallest eigenvalues of hill s operators with potentials in l 1 balls given a 1 periodic real potential q l1 r z we use 0 q to denote the smallest 1 periodic eigenvalue of the hill s equation x q t x 0 let b1 r be the ball centered at 0 of radius r in the l1 space l1 r z it is trivial that sup 0 q q b1 r r for all r 0 based on continuity of 0 q in q with the weak topology and continuous differentiability of 0 q in q with the l1 norm 1 we will apply scaling technique variational approach to extremal values in lp balls singular integrals and the limiting approach as p 1 to obtain i 0 q is bounded for q in any bounded set of l1 r z 1 and ii the minimal value l1 r inf 0 q q l1 r z q 1 r inf 0 q q l1 r z q 1 r is simply z0 1 r where z0 x 2 xtanh x 2 x 0 the extremal values of the smallest neumann eigenvalues for potentials in l1 balls are also found explicitly

asymptotic behavior of stability regions for hill s equation the asymptotic behavior of the solutions of hill s equation u e lambda 2 q x u 0 is determined for large positive real values of the coupling constant lambda 2 and large real values of the energy e the locations and widths of the stability bands and instability gaps are found the band widths are shown to decrease exponentially as lambda increases when lambda 2 e lies between the minimum and maximum values of the periodic potential q x the gap widths decrease exponentially with lambda when lambda 2 e is greater than the maximum of q x for lambda 2 e asymptotically equal to the maximum of q x the width of the nth band is asymptotically half the width of the nth gap the exponentially small band and gap widths are related to the exponentially small transmission and reflection coefficients associated with one period of q x the present results extend previous ones of meixner and schafke harrell and the authors in which lam

functional coefficient instrumental variables models we consider estimation of nonparametric structural models under a functional coefficient representation for the regression function under this representation models are linear in the endogenous components with coefficients given by unknown functions of the predetermined variables a nonparametric generalization of random coefficient models the functional coefficient restriction is an intermediate approach between fully nonparametric structural models that are ill posed when endogenous variables are continuously distributed and partially linear models over which they have appreciable flexibility we propose two step estimators that use local linear approximations in both steps the first step is to estimate a vector of reduced forms of regression models and the second step is local linear regression using the estimated reduced forms as regressors our large sample results include consistency and asymptotic normality of the proposed estimators the high practical power of estimators is illustrated via both a monte carlo simulation study and an application to returns to education

an energy momentum map for the time reversal symmetric 1 1 resonance with z 2 z 2 symmetry abstract we present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1 1 resonant hamiltonian normal forms invariant under z 2 z 2 symmetry the rich structure of these classical systems is investigated both with a singularity theory approach and geometric methods the geometric approach readily allows to find an energy momentum map describing the phase space structure of each member of the family and a catastrophe map that captures its global features quadrature formulas for the actions periods and rotation number are also provided

resonance tongues and instability pockets in the quasi periodic hill schrodinger equation this paper concerns hill s equation with a parametric forcing that is real analytic and quasi periodic with frequency vector d and a frequency or energy parameter a and a small parameter b the 1 dimensional schrodinger equation with quasi periodic potential occurs as a particular case in the parameter plane 2 a b for small values of b we show the following the resonance tongues with rotation number frac 1 2 langle bf k omega rangle bf k in mathbb z d have c boundary curves our arguments are based on reducibility and certain properties of the schrodinger operator with quasi periodic potential analogous to the case of hill s equation with periodic forcing i e d 1 several further results are obtained with respect to the geometry of the tongues one result regards transversality of the boundaries at b 0 another result concerns the generic occurrence of instability pockets in the tongues in a reversible near mathieu case that may depend on several deformation parameters these pockets describe the generic opening and closing behaviour of spectral gaps of the schrodinger operator in dependence of the parameter b this result uses a refined averaging technique also consequences are given for the behaviour of the lyapunov exponent and rotation number in dependence of a for fixed b

chaotic dynamics of a free particle interacting linearly with a harmonic oscillator we study the closed hamiltonian dynamics of a free particle moving on a ring over one section of which it interacts linearly with a single harmonic oscillator on the basis of numerical and analytical evidence we conjecture that at small positive energies the phase space of our model is completely chaotic except for a single region of complete integrability with a smooth sharp boundary showing no kam type structures of any kind this results in the cleanest mixed phase space structure possible in which motions in the integrable region and in the chaotic region are clearly separated and independent of one another for certain system parameters this mixed phase space structure can be tuned to make either of the two components disappear leaving a completely integrable or completely chaotic phase space for other values of the system parameters additional structures appear such as kam like elliptic islands and one parameter families of parabolic periodic orbits embedded in the chaotic sea the latter are analogous to bouncing ball orbits seen in the stadium billiard the analytical part of our study proceeds from a geometric description of the dynamics and shows it to be equivalent to a linked twist map on the union of two intersecting disks

extremal values of eigenvalues of sturm liouville operators with potentials in l 1 balls abstract this paper is a continuation of zhang m zhang continuity in weak topology higher order linear systems of ode sci china ser a 51 2008 1036 1058 m zhang extremal values of smallest eigenvalues of hill s operators with potentials in l 1 balls j differential equations 246 2009 4188 4220 given a potential q l p 0 1 r p 1 we use m q to denote the m th dirichlet eigenvalue of the sturm liouville operator with potential q t where m n the minimal value l m p r and the maximal value m m p r of m q with potentials q in the l p ball of radius r are well defined in this paper we will exploit the continuity of m q in q with weak topologies and the variational method to give characterizations of l m p r and m m p r when p 1 by using the limiting approach as p 1 we find that the most important extremal values l m 1 r and m m 1 r can be evaluated explicitly using some elementary functions of r the corresponding extremal problems for neumann eigenvalues and some periodic eigenvalues will be reduced to l m p r and m m p r

the hausdorff dimension of small divisors for lower dimensional kam tori given a bounded domain note see the image of page 359 for this formatted text omega subset r m and a lipschitz map note see the image of page 359 for this formatted text phi omega mapsto r n we determine the hausdorff dimension of sets of points omega in omega for which the inequality k cdot omega l cdot phi omega psi k l has infinitely many distinct integer solutions note see the image of page 359 for this formatted text k l in z m times z n satisfying l leq h where h is a fixed integer these sets interpolate between the cases h 0 and h infty which occur in the metric theory of diophantine approximation of independent and dependent quantities respectively they arise for example in the perturbation theories of lower dimensional tori in nearly integrable hamiltonian systems kam theory among others it turns out that their hausdorff dimension is independent of h and n it only depends on m and the lower order of psi at infinity part of this result even extends to the case n infty of infinite co dimension which is relevant in the kam theory of certain nonlinear partial differential equations

the indian rope trick for a parametrically excited flexible rod linearized analysis it is well known that if a column exceeds a certain critical length it will when placed upright buckle under its own weight in a recent experiment mullin has demonstrated that a column that is l

absolute continuity of symmetric markov processes we study girsanov s theorem in the context of symmetric markov processes extending earlier work of fukushima takeda and fitzsimmons on girsanov transformations of gradient type we investigate the most general girsanov transformation leading to another symmetric markov process this investigation requires an extension of the forward backward martingale method of lyons zheng to cover the case of processes with jumps

panel data discrete choice models with lagged dependent variables in this paper we consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables lags of the endogenous dependent variable as well as unobservable individual specific effects for the binary logit model with the dependent variable lagged only once chamberlain 1993 gave conditions under which the model is not identified we present a stronger set of conditions under which the parameters of the model are identified the identification result suggests estimators of the model and we show that these are consistent and asymptotically normal although their rate of convergence is slower than the inverse of the square root of the sample size we also consider identification in the semiparametric case where the logit assumption is relaxed we propose an estimator in the spirit of the conditional maximum score estimator manski 1987 and we show that it is consistent in addition we discuss an extension of the identification result to multinomial discrete choice models and to the case where the dependent variable is lagged twice finally we present some monte carlo evidence on the small sample performance of the proposed estimators for the binary response model

uniqueness of generalized schrodinger operators and applications abstract we prove necessary and sufficient conditions on r d r 0 a e so that the operator s 2 1 w1 n has exactly one self adjoint extension on w1 p which generates a sub markovian semigroup on w1 n these conditions are shown to be always fulfilled if d 1 and are verified for a large class of functions if d 1 we also prove an infinite dimensional analogue of this result where r d is replaced by some topological vector space e and the lebesgue measure dx by a gaussian measure the role of is taken by some ornstein uhlenbeck operator with general linear drift and dom s bounded smooth cylinder functions both results are derived as special cases from a general perturbation result we also give the corresponding probabilistic version i e we prove uniqueness for the associated martingale problem we present in some detail applications to the case where is a ground state of a hamiltonian in quantum field theory settling a problem which has been open for some time furthermore we apply our results to prove uniqueness in distribution of the diffusion first constructed by g jona lasinio and p k mitter for the stochastic quantization of f 2 field theory

quasi periodic stability of normally resonant tori we study quasi periodic tori under a normal internal resonance possibly with multiple eigenvalues two non degeneracy conditions play a role the first of these generalizes invertibility of the floquet matrix and prevents drift of the lower dimensional torus the second condition involves a kolmogorov like variation of the internal frequencies and simultaneously versality of the floquet matrix unfolding we focus on the reversible setting but our results carry over to the hamiltonian and dissipative contexts

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

transition curves for the quasi periodic mathieu equation in this work we investigate an extension of mathieu s equation the quasi periodic qp mathieu equation given by ddot psi delta eps cos t cos omega t psi 0 for small eps and irrational omega of interest is the generation of stability diagrams that identify the points or regions in the delta omega parameter plane for fixed eps for which all solutions of the qp mathieu equation are bounded numerical integration is employed to produce approximations to the true stability diagrams both directly and through contour plots oflyapunov exponents in addition we derive approximate analytic expressions for transition curves using two distinct techniques 1 a regular perturbation method under which transition curves delta delta omega eps are each expanded in powers of eps and 2 the method of harmonic balance utilizing hill s determinants both analytic methods deliver results in good agreement with those generated numerically in the sense that pre

stochastic differential equations for dirichlet processes we consider the stochastic differential equation dxt a xt dwt b xt dt where w is a one dimensional brownian motion we formulate the notion of solution and prove strong existence and pathwise uniqueness results when a is in c1 2 and b is only a generalized function for example the distributional derivative of a holder function or of a function of bounded variation when b aa that is when the generator of the sde is the divergence form operator a result on non existence of a strong solution and non pathwise uniqueness is given as well as a result which characterizes when a solution is a semimartingale or not we also consider extensions of the notion of stratonovich integral

rank estimation of a generalized fixed effects regression model abstract this paper considers estimation of a fixed effects version of the generalized regression model of han 1987 journal of econometrics 35 303 316 the model allows for censoring places no parametric assumptions on the error disturbances and allows the fixed effects to be correlated with the covariates we introduce a class of rank estimators that consistently estimate the coefficients in the generalized fixed effects regression model the maximum score estimator for the binary choice fixed effects model is part of this class like the maximum score estimator the class of rank estimators converge at less than the n rate smoothed versions of these estimators however converge at rates approaching the n rate in a version of the model that allows for truncated data a sufficient condition for consistency of the estimators is that the error disturbances have an increasing hazard function

some results on the dynamics of the linear parametric oscillator with general time varying frequency the dynamics of single degree of freedom linear oscillators under parametric excitation of general type periodic or non periodic is considered an analytical approach based on complexification and amplitude phase decomposition of the response is developed leading to an exact set of first order ordinary differential equations governing the amplitude and phase of the motion perturbation schemes for solving this set are developed and the solutions of the derived modulation equation are outlined in addition some results and comments on the stability of the derived solutions are provided

absolute continuity of symmetric diffusions let x and y be symmetric diffusion processes with a common state space and let p m resp q be the law of x resp y with its symmetry measure m resp as initial distribution we study the consequences of the absolute continuity condition q t 1 t the density p also serves to link the dirichlet forms of x and y in a simple way our identification of l relies on notions of even and odd for additive functionals these notions complement fukushima s decomposition and the forward backward martingale decomposition of lyons and zheng

persistence of lower dimensional hyperbolic tori for reversible system abstract in this paper we consider the persistence of hyperbolic lower dimensional invariant tori with prescribed frequency for reversible system and prove that if the frequency mapping has nonzero topological degree at some diophantine frequency then the hyperbolic lower invariant dimensional torus with this frequency persists under small perturbations

probabilistic description of extreme events in intermittently unstable dynamical systems excited by correlated stochastic processes massachusetts institute of technology naval engineering education center grant 3002883706

the finite dimensional reversible kam theory abstract the main results of the theory of quasi periodic motions in finite dimensional reversible dynamical systems are surveyed lower dimensional invariant tori and excitation of elliptic normal modes are discussed in detail the case where the reversing involution is perturbed is considered several fundamental differences between the reversible and hamiltonian theories are listed

equivariant singularity theory with distinguished parameters two case studies of resonant hamiltonian systems we consider hamiltonian systems near equilibrium that can be formally reduced to one degree of freedom spatiotemporal symmetries play a key role the planar reduction is studied by equivariant singularity theory with distinguished parameters the method is illustrated on the conservative spring pendulum system near resonance where it leads to integrable approximations of the iso energetic poincare map the novelty of our approach is that we obtain information on the whole dynamics regarding the quasi periodic solutions the global configuration of their invariant manifolds and bifurcations of these

hill s equation with a large potential we obtain asymptotic expansions for large values of the parameter lambda of the stability boundaries the stability band widths the floquet multipliers and the solutions of hill s equation left frac d 2 dx 2 lambda 2 q x t right u eu the potential q x is assumed to be periodic and to have a unique global minimum within each period at which q 0 the results for the stability band widths show that they decay exponentially with lambda as lambda increases these results generalize those for symmetric potentials due to harrell and that for the mathieu equation due to meixner and schafke

resonance tongue interaction in the parametrically excited column this paper concerns a codimension two analysis of the interaction between various resonances that occur in an upright flexible rod subject to sinusoidal parametric excitation particular attention is paid to rods that are just longer than their critical length for self weight buckling and their possible stabilization by the excitation previous work has identified three small dimensionless parameters in this problem the closeness of the length divided by the cube root of bending stiffness to the critical one the amplitude of excitation and the reciprocal of the frequency of excitation multiple timescale analysis is used to show how the asymptotics of resonance tongues in the amplitude versus bending stiffness plane becomes of lower order at certain special values of the frequency ratio where two resonances interact in particular an o 1 change in the shape of the parameter region of the stabilized supercritical rod occurs through interaction with the pure harmonic resonance of some other mode of

simple estimators for nonparametric panel data models with sample attrition abstract this paper considers a multiperiod random effects panel model with attrition of observations over the panel allowing for flexible regressions unknown distributions and attrition in one period to be followed by reappearance in a future period in each time period the regression in the retained data is additive in the function of interest and a time varying correction term that depends on the contemporaneous probability of retention in the sample these retention probabilities themselves depend on a regressor vector that grows with time in particular for the t th and t s th periods these vectors differ by exactly s terms the paper gives two step estimators that correct for attrition bias by including estimates of these retention probabilities one for each period that experiences attrition asymptotic normality for a class of functionals of the model is derived also including as special cases the linear and partially linear versions of the model

poisson structure of the reversible 1 1 resonance abstract vector fields that are reversible but non hamiltonian are considered in the neighborhood of a 1 1 resonance it is found that the normalized vector field has a hidden poisson structure on the orbit space that is reminiscent of the equations governing the rigid body in mechanics the theory is used to give a geometric characterization of the phase space in the neighborhood of a reversible 1 1 resonance certain similarities and also essential differences with the hamiltonian 1 1 resonance are found

resonance tongues in hill s equations a geometric approach abstract the geometry of resonance tongues is considered in mainly reversible versions of hill s equation close to the classical mathieu case hill s map assigns to each value of the multiparameter the corresponding poincare matrix by an averaging method the geometry of hill s map locally can be understood in terms of cuspoid whitney singularities this adds robustness to the result the algorithmic nature of the averaging method enables a pull back to the resonance tongues of the original system

unusual lienard type nonlinear oscillator a lienard type nonlinear oscillator of the form x kxx k2 9 x3 lambda1x 0 which may also be considered as a generalized emden type equation is shown to possess unusual nonlinear dynamical properties it is shown to admit explicit nonisolated periodic orbits of conservative hamiltonian type for lambda1 0 these periodic orbits exhibit the unexpected property that the frequency of oscillations is completely independent of amplitude and continues to remain as that of the linear harmonic oscillator this is completely contrary to the standard characteristic property of nonlinear oscillators interestingly the system though appears deceptively a dissipative type for lambda1 or 0 does admit a conserved hamiltonian description where the characteristic decay time is also independent of the amplitude the results also show that the criterion for conservative hamiltonian system in terms of divergence of flow function needs to be generalized

non symmetric perturbations of symmetric dirichlet forms abstract we provide a path space integral representation of the semigroup associated with the quadratic form obtained by lower order perturbation of a symmetric local dirichlet form the representation is a combination of feynman kac and girsanov formulas and extends previously known results in the framework of symmetric diffusion processes through the use of the hardy class of smooth measures which contains the kato class of smooth measures

analytical periodic solution and stability assessment of 1 dof parametric systems with time varying stiffness the presented paper deals with an approach to analytical periodic solution and to stability assessment of one degree of freedom linear vibrating systems it is supposed that these systems are excited by the time periodic force and contain time periodic stiffness the periodic green s function determined as a response to a dirac chain of unit impulses repeating with period of excitation is used to transform the equation of motion into the fredholm integral equation with degenerated kernel if the dirac chain is expressed as a fourier series and a limited number of terms is taken into account the solution of the integral equation can also be obtained in a series form it has been found that the real eigenvalues of the system matrix determine the critical values of the fluctuation stiffness parameter the values of this real parameter correspond to the borders of in stability in the plane given by the variation of the angle frequency and of the fluctuation stiffness parameter moreover very interesting property of the system matrix was observed the positive sign of the real valued determinant of the system matrix means the existence of periodic solution system is stable in the opposite case the periodic solution does not exist system is unstable the verification of obtained results was performed on two case studies the floquet method was used to validate the stability assessment presented analytical periodic solution was compared with steady state obtained by the runge kutta continuation a very good agreement was achieved in both cases

poincare inequality for weighted first order sobolev spaces on loop spaces abstract let e be the loop space over a compact connected riemannian manifold with a torsion skew symmetric connection let l d be the ornstein uhlenbeck operator on a nonempty connected component d of the loop space e and let v d r be the restriction on d of the potential in the logarithmic sobolev inequality found by l gross on the loop group by s aida and by f z gong and z m ma on the loop space respectively we prove that the schrodinger operator l v l d v always has a spectral gap at the bottom 0 v of its spectrum and thus has its ground state transformed operator 1 l v 0 v where is the unique ground state of l v in particular our result proves l gross s conjecture about the existence of a spectral gap for the ground state transform of the schrodinger operator studied by him on the loop group in addition in all the above cases we identify the domain of the dirichlet forms associated with the ground state transforms as weighted first order sobolev spaces with weight given by 2 thus establishing a poincare inequality for them all these results are consequences from some new results in this paper on dirichlet forms characterizing certain classes with spectral gaps and from results by s aida and m hino

nonparametric estimation with nonlinear budget sets choice models with nonlinear budget sets provide a precise way of accounting for the nonlinear tax structures present in many applications in this paper we propose a nonparametric approach to estimation of these models the basic idea is to think of the choice in our case hours of labor supply as being a function of the entire budget set then we can do nonparametric regression where the variable in the regression is the budget set we reduce the dimensionality of this problem by exploiting structure implied by utility maximization with piecewise linear convex budget sets this structure leads to estimators where the number of segments can differ across observations and does not affect accuracy we give consistency and asymptotic normality results for these estimators the usefulness of the estimator is demonstrated in an empirical example where we find it has a large impact on estimated effects of the swedish tax reform

the stochastic mathieu s equation in this manuscript we consider generalizations of the classical mathieu s equation to stochastic systems unlike previous works we focus on internal frequencies that vary continuously between periodic and stochastic variables by numerically integrating the system of equations using a symplectic method we determine the lyapunov exponents for a wide range of parameters to quantify how the growth rates vary in parameter space in the nearly periodic limit we recover the same growth rates as the classical mathieu s equation as the stochasticity increases the maximum growth decreases and the unstable region broadens which signifies that the stochasticity can both stabilize and destabilize a system in relation to the deterministic limit in addition to the classical parametric modes there is also an unstable stochastic mode that arises only for moderate stochasticity the power spectrum of the solutions shows that an increase in stochasticity tends to narrow the width of the subharmonic peak and increase the decay away from this peak

a non homogeneous hill s equation the existence of periodic solutions for a forced hill s equation is proved the proof is then extended to the case of a non homogeneous matrix valued hill s equation under the stated conditions using lyapunov s criteria proc ams 13 1962 601 hill s equation interscience publishers new york 1966 some results on the stability oh hill s equation are obtained

varying coefficient panel data model in the presence of endogenous selectivity and fixed effects this paper considers a exible panel data sample selection model in which i the outcome equation is permitted to take a semiparametric varying coecient form to capture potential parameter heterogeneity in the relationship of interest ii both the outcome and parametric selection equations contain unobserved xed eects and iii selection is generalized to a polychotomous case we propose a two stage estimator given consistent parameter estimates from the selection equation obtained in the rst stage we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time the selection bias term is then asymptotically removed from the equation along with xed eects using kernel based weights the proposed estimator is consistent and asymptotically normal we rst investigate the nite sample properties of the estimator in a small monte carlo study and then apply it to study production technologies of u s retail credit unions from 2002 to 2006

markov processes and nonsymmetric dirichlet forms without regularity we study right markov processes in weak duality satisfying the sector condition of silverstein dirichlet space techniques are employed but without the customary c0 regularity hypothesis nonetheless the potential theory of such processes is quite amenable in particular it is proved that semipolar sets are quasi polar this extends results of silverstein and lejan

normal forms and unfoldings of linear systems in eigenspaces of anti automorphisms of order two abstract in this article we classify normal forms and unfoldings of linear maps in eigenspaces of anti automorphisms of order two our main motivation is provided by applications to linear systems of ordinary differential equations general and hamiltonian which have both time preserving and time reversing symmetries however the theory gives a uniform method to obtain normal forms and unfoldings for a wide variety of linear differential equations with additional structure we give several examples and include a discussion of the phenomenon of orbit splitting as a consequence of orbit splitting we observe passing and splitting of eigenvalues in unfoldings

panel data and unobservable individual effects abstract an important purpose in pooling time series and cross section data is to control for individual specific unobservable effects which may be correlated with other explanatory variables e g latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions using instrumental variables and the time invariant characteristics of the latent variable we derive 1 1 a test for the presence of this effect and for the over identifying restriction we use 2 2 necessary and sufficient conditions for identification of all the parameters in the model and 3 3 the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within groups estimator we calculate efficient estimates of a wage equation from the michigan income dynamics data which indicate substantial differences from within groups and balestra nerlove estimates particularly a significantly higher estimate of the returns to schooling

analytic characterization of conditional gaugeability for non local feynman kac transforms abstract an analytic characterization of gaugeability and conditional gaugeability is given for non local or discontinuous feynman kac transforms of general symmetric markov processes this analytic characterization is very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases

continuity in weak topology and extremal problems of eigenvalues of the p laplacian we will study the dependence of eigenvalues of the one dimensional p laplacian on potentials or weights two results are obtained one is the continuity of eigenvalues in potentials with respect to the weak topologies of l spaces 1 and the other is the continuous differentiability of eigenvalues in potentials with respect to l norms as applications we will study some extremal problems of eigenvalues by developing some analytical methods

mating siegel quadratic polynomials 1 1 mating definitions and some history mating quadratic polynomials is a topological construction suggested by douady and hubbard do2 to partially parametrize quadratic rational maps of the riemann sphere by pairs of quadratic polynomials some results on matings of higher degree maps exist but we will not discuss them in this paper while there exist several presumably equivalent ways of describing the construction of mating the following approach is perhaps the most standard consider two monic quadratic polynomials fi and f2 whose filled julia sets k fi are locally connected for each fi let di denote the conformal isomorphism between the basin of infinity c k f and c ed with i 00 00 and v oo 1 these bottcher maps conijugate the polynomials to the squaring map

on reflected dirichlet spaces reflecting diffusion processes on smooth domains in euclidean space are well understood silverstein in 22 and 23 developed two variant procedures for constructing the reflected processes for a general class of symmetric hunt processes from a dirichlet space point of view a direct approach is given in this paper and these two variant procedures are shown to yield the same result only the techniques of martingales and ordinary markov processes are used

computing the stability regions of hill s equation a numerical scheme is presented for computing the boundaries between the stable and unstable regions of hill s equation the approach based on formulating an integral representation of hill s equation thus the problem of finding the boundary between the stable and unstable regions in parameter space is then a spectral problem of an integral operator several properties of the operator are derived and an iteration scheme for numerical calculation of the stability boundary is presented the numerical scheme has a number of advantages over the classical methods for locating the stability boundary several examples are presented

versal deformations and normal forms for reversible and hamiltonian linear systems the problem of this article is the characterization of equivalence classes and their versal deformations for reversible and reversible hamiltonian matrices in both cases the admissible transformations form a subgroup g of gl m therefore the gl m orbits of a given matrix may split into several g orbits these orbits are characterized by signs for each sign we have a normal form and a corresponding versal deformation the main tool in the characterization is reduction to the semi simple case c 1996 academic press inc

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

an elasticity can be estimated consistently without a priori knowledge of functional form we consider an open question in applied price theory without a priori knowledge of a firm s cost function or a consumer s indirect utility function is it possible to estimate price and substitution elasticities consistently by observing a demand system as the work of white 30 guilkey lovell and sickles 19 and others has shown ordinary flexible functional forms such as the translog cannot achieve this objective we find that if one is prepared to assume that elasticities of substitution cannot oscillate wildly over the region of interest then consistent estimation is possible using the fourier flexible form provided the number of fitted parameters increases as the number of observations increases this result obtains with any of the commonly used statistical methods as for example multivariate least squares maximum likelihood and three stage least squares it obtains if the number of fitted parameters is chosen adaptively by observing the data or chosen deterministically according to some fixed rule we approach the problem along the classical lines of estimability considerations as used in the study of less than full rank linear statistical models and thereby discover that the problem has a fascinating structure which we explore in detail

identification and sequential estimation of panel data models with insufficient exclusion restrictions abstract this paper presents estimators for nonparametric panel data models with additive fixed effects we analyze a model in which the entire regressor vector consisting of time varying as well as time invariant regressors is correlated with the individual fixed effect but there are insufficient exclusion restrictions to permit direct instrumental variables estimation of the model it is shown that when the model satisfies the additive interactive regression air representation of andrews and whang economic theory 6 1990 466 480 a sequential estimator consistently estimates the model the limiting distribution of scalar nonlinear functionals of the model is shown to be standard normal finite sample properties of the estimator are considered in a monte carlo simulation study and used to estimate the returns to education in a cohort of mature men from the national longitudinal survey

the inverted pendulum a singularity theory approach the inverted pendulum with small parametric forcing is considered as an example of a wider class of parametrically forced hamiltonian systems the qualitative dynamics of the poincare map corresponding to the central periodic solution is studied via an approximating integrable normal form at bifurcation points we construct local universal models in the appropriate symmetry context using equivariant singularity theory in this context structural stability can be proved under generic conditions

normal linear stability of quasi periodic tori abstract we consider families of dynamical systems having invariant tori that carry quasi periodic motions our interest is the persistence of such tori under small nearly integrable perturbations this persistence problem is studied in the dissipative the hamiltonian and the reversible setting as part of a more general kam theory for classes of structure preserving dynamical systems this concerns the parametrized kam theory as initiated by moser j k moser on the theory of quasiperiodic motions siam rev 8 2 1966 145 172 j k moser convergent series expansions for quasi periodic motions math ann 169 1967 136 176 and further developed in g b huitema unfoldings of quasi periodic tori phd thesis university of groningen 1988 h w broer g b huitema f takens unfoldings of quasi periodic tori mem amer math soc 83 421 1990 1 82 h w broer g b huitema unfoldings of quasi periodic tori in reversible systems j dynam differential equations 7 1 1995 191 212 the corresponding nondegeneracy condition involves certain trans versality conditions on the normal linear leading part at the invariant tori we show that as a consequence a cantor family of diophantine tori with positive hausdorff measure is persistent under nearly integrable perturbations this result extends the above references since presently the case of multiple floquet exponents is included our leading example is the normal 1 1 resonance which occurs a lot in applications both hamiltonian and reversible as an illustration of this we briefly describe the lagrange top coupled to an oscillator

stability analysis of linear systems subject to regenerative switchings this paper investigates the stability of switched linear systems whose switching signal is modeled as a stochastic process called a regenerative process we show that the mean stability of such a switched system is characterized by the spectral radius of a matrix the matrix is obtained by taking the expectation of the transition matrix of the system on one cycle of the underlying regenerative process the characterization generalizes floquet s theorem for the stability analysis of linear time periodic systems we illustrate the result with the stability analysis of a linear system with a failure prone controller under periodic maintenance

the quasi periodic centre saddle bifurcation abstract nearly integrable families of hamiltonian systems are considered in the neighbourhood of normally parabolic invariant tori in the integrable case such tori bifurcate into normally elliptic and normally hyperbolic invariant tori with a kam theoretic approach it is shown that both the normally parabolic tori and the bifurcation scenario survive a non integrable perturbation parametrised by pertinent large cantor sets these results are applied to rigid body dynamics