a weakly monotonic backward induction algorithm on finite bounded subsets of vector lattices we present a new efficient and robust backward induction algorithm which is weakly monotonic working on bounded subsets without holes of lattices we prove all its properties give examples of applications and illustrate its behavior comparing it with the natural extension of the unidimensional algorithm presented in puterman markov decision processes discrete stochastic dynamic programming wiley new york 1994 in the sense of topkis frontiers of economic research series princeton university press princeton nj 1998 and white recent developments in markov decision processes academic press new york 1980 261 and showing also experimentally that it is much more efficient

new simple lie superalgebras in characteristic 3 abstract symplectic respectively orthogonal triple systems provide constructions of lie algebras respectively superalgebras however in characteristic 3 it is shown that this role can be interchanged and that lie superalgebras respectively algebras can be built out of symplectic triple systems respectively orthogonal triple systems with a different construction as a consequence new simple finite dimensional lie superalgebras as well as new models of some nonclassical simple lie algebras over fields of characteristic 3 will be obtained

recent fluid deformation closure for velocity gradient tensor dynamics in turbulence timescale effects and expansions abstract in order to model pressure and viscous terms in the equation for the lagrangian dynamics of the velocity gradient tensor in turbulent flows chevillard meneveau l chevillard c meneveau lagrangian dynamics and geometric structure of turbulence phys rev lett 97 174501 2006 1 4 introduced the recent fluid deformation closure using matrix exponentials the closure allows us to overcome the unphysical finite time blow up of the well known restricted euler model however it also requires the specification of a decorrelation timescale of the velocity gradient along the lagrangian evolution and when the latter is chosen too short or equivalently the reynolds number is too high the model leads to unphysical statistics in the present paper we explore the limitations of this closure by means of numerical experiments and analytical considerations we also study the possible effects of using time correlated stochastic forcing instead of the previously employed white noise forcing numerical experiments show that reducing the correlation timescale specified in the closure and in the forcing does not lead to a commensurate reduction of the autocorrelation timescale of the predicted evolution of the velocity gradient tensor this observed inconsistency could explain the unrealistic predictions at increasing reynolds numbers we perform a series expansion of the matrix exponentials in powers of the decorrelation timescale and we compare the full original model with a linearized version the latter is not able to extend the limits of applicability of the former but allows the model to be cast in terms of a damping term whose sign gives additional information about the stability of the model as a function of the second invariant of the velocity gradient tensor

triple products and yang baxter equation i octonionic and quaternionic triple systems the yang baxter equation can be recast as a triple product equation assuming the triple product to satisfy some algebraic relations new solutions of the yang baxter equation can be found this program has been completed here for the simplest triple systems which are called octonionic and quaternionic the solutions are of rational type

on the cartan jacobson theorem abstract the well known cartan jacobson theorem claims that the lie algebra of derivations of a cayley algebra is central simple if the characteristic is not 2 or 3 in this paper we have studied these two cases with the following results if the characteristic is 2 the theorem is also true but if the characteristic is 3 the derivation algebra is not simple we have also proved that in this last case there is a unique nonzero proper seven dimensional ideal which is a central simple lie algebra of type a2 and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic as a lie algebra to the ideal itself the original motivation of this work was a series of computer aided calculations which proved the simplicity of derivation algebras of cayley algebras in the case of characteristic not 3 these computations also proved the existence of a unique nonzero proper ideal which turns out to be seven dimensional in the algebra of derivations of split cayley algebras in characteristic 3

accuracy of simulations for stochastic dynamic models this paper is concerned with accuracy properties of simulations of approximate solutions for stochastic dynamic models our analysis rests upon a continuity property of invariant distributions and a generalized law of large numbers we then show that the statistics generated by any sufficiently good numerical approximation are arbitrarily close to the set of expected values of the model s invariant distributions also under a contractivity condition on the dynamics we establish error bounds these results are of further interest for the comparative study of stationary solutions and the estimation of structural dynamic models

an extended freudenthal magic square in characteristic 3 abstract freudenthal s magic square which in characteristic 0 contains the exceptional lie algebras other than g 2 is extended over fields of characteristic 3 through the use of symmetric composition superalgebras to a larger square that contains both lie algebras and superalgebras with one exception the simple lie superalgebras that appear have no counterpart in characteristic 0

nonparametric tests for and against likelihood ratio ordering in the two sample problem we derive nonparametric procedures for testing for and against likelihood ratio ordering in the two population setting with continuous distributions we account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood estimators of the continuous distribution functions f and g in particular we focus on testing equality of f and g versus likelihood ratio ordering and testing for a violation of likelihood ratio ordering for both testing problems we propose area based and sup norm based test statistics derive appropriate limiting distributions and provide simulation results that characterise the performance of our procedures we illustrate our methods using data from a controlled experiment involving the effects of radiation on mice

stochastic monotonicity and stationary distributions for dynamic economies the existence and stability of invariant distributions for stochastically monotone processes is studied the knaster tarski fixed point theorem is applied to establish existence of fixed points of mappings on compact sets of measures that are increasing with respect to a stochastic ordering global convergence of a monotone markov process to its unique invariant distribution is established under an easily verified assumption topkis theory of supermodular functions is applied to stochastic dynamic optimization providing conditions under which optimal stationary decisions are monotone functions of the state and induce a monotone markov process applications of these results to investment theory stochastic growth and industry equilibrium dynamics are given

models of the octonions and g2 different models of the cayley algebras and of their lie algebras of derivations are given based on some distinguished subalgebras of the later ones

on nondifferentiable functions and the bootstrap we investigate a class of statistical problems where usual bootstrap methods fail and discuss two alternative solutions in particular a stochastic procedure for constructing confidence sets is proposed special applications are the eigenvalues of a covariance matrix and minimum distance functionals

monotonic robust optimal control policies for the time quality trade offs in concurrent new product development npd recent research suggests that new product specifications evolve during its realization in this paper we introduce a nonstationary markovian model that supports the dynamic achievement of the new product definition without precedence constraints taking into account both market and technological uncertainty we use lattice programming techniques to prove the existence of a nondecreasing monotonic optimal policy thus we enable a more efficient computation of optimal policies of the markov decision process we also prove that the monotonic optimal paths are robust to the variation of key parameters as the solving rate of the design activities and the safety margin for achieving the new product at the deadline

scale dependence of the coarse grained velocity derivative tensor structure in turbulence velocity fluctuations in hydrodynamic turbulence have a nontrivial structure characterized by correlations of the velocity gradient tensor in this paper we consider a phenomenological model incorporating the main features of hydrodynamic fluid turbulence aimed at predicting the structure of the velocity gradient tensor m coarse grained at a spatial scale r this model m chertkov a pumir and b i shraiman phys fluids 11 2394 1999 is formulated as a set of stochastic ordinary differential equations with three dimensionless parameters characterizing the reduction of the nonlinearity induced by the pressure term the reisotropization effect of the small scale velocity field and the influence of the small scales on the coarse grained velocity derivative tensor semiclassical solutions of this model are obtained and compared with direct numerical simulations dns data the dns data show that the joint probability distribution function of the second and third invariants of m becomes increasingly skewed as the scale r decreases in the inertial range the model results correctly reproduce this behavior provided the parameter that controls nonlinearity reduction is finely tuned the influence of the other parameters in the model is much weaker

affine connections on 3 sasakian and manifolds the space of invariant affine connections on every 3 sasakian homogeneous manifold of dimension at least seven is described in particular the subspace of invariant affine metric connections and the subclass with skew torsion are also determined to this aim an explicit construction of all 3 sasakian homogeneous manifolds is exhibited it is shown that the 3 sasakian homogeneous manifolds which admit nontrivial einstein with skew torsion invariant affine connections are those of dimension seven that is mathbb s 7 mathbb r p 7 and the aloff wallach space mathfrak w 7 1 1 on mathbb s 7 and mathbb r p 7 the set of such connections is bijective to two copies of the conformal linear transformation group of the euclidean space while it is strictly bigger on mathfrak w 7 1 1 the set of invariant connections with skew torsion whose ricci tensor satisfies that its eigenspaces are the canonical vertical and horizontal distributions is fully described on 3 sasakian homogeneous manifolds an affine connection satisfying these conditions is distinguished by parallelizing all the reeb vector fields associated with the 3 sasakian structure which is also einstein with skew torsion on the 7 dimensional examples the invariant metric affine connections on 3 sasakian homogeneous manifolds with parallel skew torsion have been found finally some results have been adapted to the non homogeneous setting

ordered solutions for dynamic programs suppose x indexes a collection of optimization problems in rn and x is an optimal program for the problem indexed by x x sufficient conditions are presented for two other families of optimization problems to possess optimal programs 0x and 0x for the respective problems when x x such that 0x x 0x for all x x this result is then applied to obtain bounds on an optimal policy in the class of dynamic programs which are bounded monotone contractions

zero sum ergodic stochastic games with feller transition probabilities we consider zero sum stochastic games with borel state spaces satisfying a generalized geometric ergodicity condition the main objective of this paper is to establish a minimax theorem for a class of ergodic stochastic games with the feller transition probability function all previous results on ergodic stochastic games are based on a strong continuity of the transition probabilities in the actions of the players

computing the distributions of economic models via simulation we study a monte carlo algorithm for computing marginal and stationary densities of stochastic models with the markov property establishing global asymptotic normality and op n 1 2 convergence asymptotic normality is used to derive error bounds in terms of the distribution of the norm deviation

monotone comparative statics the authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem in addition they develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm the monopolist the bertrand oligopolist consumer and growth theory game theory and general equilibrium analysis copyright 1994 by the econometric society

nonparametric estimation and inference about the overlap of two distributions this paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques this quantity has been proposed as a measure of economic polarization between two groups anderson 2004 and anderson et al 2010 in ecology it has been used to measure the overlap of species we give the asymptotic distribution theory of our estimator which in some cases of practical relevance is nonstandard due to a boundary value problem we also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider we investigate the finite sample properties of our methods by simulation methods we give an application to the study of polarization within china in recent years using household survey data from two provinces taken in 1987 and 2001 we find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space

tests of stochastic monotonicity with improved power abstract we develop improved statistical procedures for testing stochastic monotonicity while existing tests use a fixed critical value to set the limiting rejection rate equal to nominal size at the least favorable case we use a bootstrap procedure to raise the limiting rejection rate to nominal size over much of the null this improves power against relevant local alternatives to show the validity of our approach we draw on recent results on the directional differentiability of the least concave majorant operator and on bootstrap inference when smoothness conditions sufficient to apply the functional delta method for the bootstrap are not satisfied

testing for stochastic monotonicity we propose a test of the hypothesis of stochastic monotonicity this hypothesis is of interest in many applications in economics our test is based on the supremum of a rescaled u statistic we show that its asymptotic distribution is gumbel the proof is difficult because the approximating gaussian stochastic process contains both a stationary and a nonstationary part and so we have to extend existing results that only apply to either one or the other case we also propose a refinement to the asymptotic approximation that we show works much better in finite samples we apply our test to the study of intergenerational income mobility

toward an empirical analysis of polarization stochastic dominance conditions may be interpreted as a means of defining the degree and nature of separateness of two distributions by describing polarization states in terms of stochastic dominance conditions this paper presents a taxonomy of and tests for polarization both between and within population distributions four examples from the poverty growth and development wage distribution and assortative pairing literatures are used to illustrate how the techniques may be used in empirical applications

an improved bootstrap test of stochastic dominance we propose a new method of testing stochastic dominance that improves on existing tests based on the standard bootstrap or subsampling the method admits prospects involving infinite as well as finite dimensional unknown parameters so that the variables are allowed to be residuals from nonparametric and semiparametric models the proposed bootstrap tests have asymptotic sizes that are less than or equal to the nominal level uniformly over probabilities in the null hypothesis under regularity conditions this paper also characterizes the set of probabilities so that the asymptotic size is exactly equal to the nominal level uniformly as our simulation results show these characteristics of our tests lead to an improved power property in general the improvement stems from the design of the bootstrap test whose limiting behavior mimics the discontinuity of the original test s limiting distribution

estimation by simulation of monotone dynamical systems this paper offers a general proof of consistency for the simulated moments estimator in a parameterized family of stochastic models with monotone dynamics models with this monotonicity property are frequently encountered in economic applications the proof of consistency of the estimator draws upon a uniform law of large numbers over a continuum of invariant distributions indexed by the model s parameters

invariant distributions and the limiting behavior of markovian economic models equilibria in stochastic economic models are often time series which fluctuate in complex ways but it is sometimes possible to summarize the long run average characteristics of these fluctuations for example if the law of motion determined by economic interactions is markovian and if the equilibrium time series converges in a specific probabilistic sense then the long run behavior is completely determined by an invariant probability distribution this paper develops and unifies a number of results found in the probability literature which enable one to prove under very general conditions the existence of an invariant distribution and the convergence of the corresponding markov process virtually all of economic theory focuses upon the study of economic equilibrium this concept has recently undergone several subtle elaborations no longer must a system of markets in equilibrium be thought of as one at rest in a static steady state instead there is a growing body of literature e g 4 5 12 16 20 21 which defines equilibrium as a stochastic process of market clearing prices and quantities which is consistent with the self interested behavior of economic agents needless to say equilibrium stochastic processes can be very complex time series which fluctuate in irregular ways for theoretical and econometric purposes it is useful to have a convenient way of summarizing the average behavior of such processes over time this paper draws together and unifies a number of fundamental results from the probability literature which enable one to do this for discrete time markov processes on general state spaces the starting point of the analysis is a set s of economic states e g prices and or quantities the only technical restriction placed upon s is that it be a borel subset of a complete separable metric space the second datum is a transition probability p s on s the number p s a records the probability that the economic system moves from the state s to some state in the borel subset a of s during one unit of elapsed time in economic applications the transition probability is usually derived from hypotheses about market clearing and the maximizing behavior of economic agents the transition probability together with an initial probability measure on s defines a discrete time markov process one way of summarizing the dynamic behavior implied by p is to look for an invariant probability a probability measure x on s is invariant for p if for all borel subsets a of s one has the equality f p s a x ds x a an invariant probability is a kind of probabilistic steady state for the dynamics defined by p of course there may be no invariant probability for p at all and even if one exists it may convey no information about the average behavior of the process over time except under very special initial conditions there is a second way of summarizing the behavior of markov processes defined by the transition probability p let p s a denote the n step transition

distribution free tests of stochastic monotonicity this article proposes an omnibus test for monotonicity of nonpara metric conditional distributions and its moments unlike previous proposals our method does not require smooth estimation of the derivatives of nonparametric curves and it can be implemented even when probability densities do not exist in fact we only require continuity of the marginal distributions under the null and xed alternatives distinguishing features of our approach are that critical values are pivotal under the null in nite samples and the test is invariant to any monotonic continuous transformation of the explanatory variable the test sta tistic is the sup norm of the dierence between the empirical copula function and its least concave majorant with respect to the explanatory variable coordinate the resulting test is able to detect local alternatives converging to the null at the parametric rate n 1 2 with n the sample size the article also discusses several applications and extensions of the proposal these include testing monotonicity of general conditional moments and the extension to multivariate explanatory variables the nite sample performance of the test is examined by means of a monte carlo experiment

small scale vorticity filaments and structure functions of the developed turbulence abstract we develop a theory of turbulence based on the navier stokes equation without using dimensional or phenomenological considerations a small scale vortex filament is the main element of the theory the theory allows to obtain the scaling law and to calculate the scaling exponents of lagrangian and eulerian velocity structure functions in the inertial range the obtained results are shown to be in very good agreement with numerical simulations and experimental data the introduction of stochasticity into the equations and derivation of scaling exponents are discussed in details a weak dependence on statistical propositions is demonstrated the relation of the theory to the multifractal model is discussed

asymptotics of a class of markov processes which are not in general irreducible on obtient des conditions d existence de probabilites invariantes uniques pour des processus de markov qui ne sont pas en general irreductibles