on a system of klein gordon type equations with acoustic boundary conditions we prove the existence uniqueness and uniform stabilization of global solutions for a generalized system of klein gordon type equations with acoustic boundary conditions on a portion of the boundary and the dirichlet boundary condition on the rest

some nonlinear wave equations with acoustic boundary conditions abstract we prove the existence and uniqueness of global solutions to the mixed problem for the carrier equation u tt m u 2 dx u u t u t 0 with acoustic boundary conditions

universality of zipf s law zipf s law is the most common statistical distribution displaying scaling behavior cities populations or firms are just examples of this seemingly universal law although many different models have been proposed no general theoretical explanation has been shown to exist for its universality here we show that zipf s law is in fact an inevitable outcome of a very general class of stochastic systems borrowing concepts from algorithmic information theory our derivation is based on the properties of the symbolic sequence obtained through successive observations over a system with an ubounded number of possible states specifically we assume that the complexity of the description of the system provided by the sequence of observations is the one expected for a system evolving to a stable state between order and disorder this result is obtained from a small set of mild physically relevant assumptions the general nature of our derivation and its model free basis would explain the ubiquity of such a law in real systems

the frisch scheme in dynamic system identification abstract the use of the frisch scheme in the identification of linear dynamic systems is investigated in order to describe the whole family of models that can explain given input output noisy sequences unlike the algebraic case it is shown that in general only a single model is compatible with the data these results are first proposed for single input single output systems and then generalized to the multivariable case

brief paper on the identifiability of errors in variables models with white measurement errors we discuss identifiability of dynamic siso errors in variables eiv models with white measurement errors although this class of models turns out to be generically identifiable it has been pointed out that in certain circumstances there may be two eiv models which are indistinguishable from external input output experiments this lack of global identifiability may be prejudicial to identification and needs better understanding the identifiability conditions found in the literature guarantee uniqueness under certain coprimality assumptions on the rational transfer function of the ideal true system and the spectral density of the noiseless true input unfortunately these conditions are not testable since they concern precisely the unknowns of the problem which are not available to the experimenter we provide new identifiability conditions which are instead expressible in terms of the external description of the observable signals namely their joint power spectral densities

brief paper frequency domain maximum likelihood estimation of linear dynamic errors in variables models this paper studies the linear dynamic errors in variables problem for filtered white noise excitations first a frequency domain gaussian maximum likelihood ml estimator is constructed that can handle discrete time as well as continuous time models on a part s of the unit circle or imaginary axis next the ml estimates are calculated via a computationally simple and numerically stable gauss newton minimization scheme finally the cramer rao lower bound is derived

average is over abstract the popular perception of statistical distributions is depicted by the iconic bell curve which comprises of a massive bulk of middle class values and two thin tails one of small left wing values and one of large right wing values the shape of the bell curve is unimodal and its peak represents both the mode and the mean thomas friedman the famous new york times columnist recently asserted that we have entered a human era in which average is over in this paper we present mathematical models for the phenomenon that friedman highlighted while the models are derived via different modeling approaches they share a common foundation inherent tipping points cause the models to phase shift from a normal bell shape statistical behavior to an anomalous statistical behavior the unimodal shape changes to an unbounded monotone shape the mode vanishes and the mean diverges hence i there is an explosion of small values ii large values become super large iii middle class values are wiped out leaving an infinite rift between the small and the super large values and iv average is over indeed

lorenzian analysis of infinite poissonian populations and the phenomena of paretian ubiquity abstract the lorenz curve is a universally calibrated statistical tool measuring quantitatively the distribution of wealth within human populations we consider infinite random populations modeled by inhomogeneous poisson processes defined on the positive half line the randomly scattered process points representing the wealth of the population members or any other positive valued measure of interest such as size mass energy etc for these populations the notion of macroscopic lorenz curve is defined and analyzed and the notion of lorenzian fractality is defined and characterized we show that the only non degenerate macroscopically observable lorenz curves are power laws manifesting paretian statistics thus providing a universal lorenzian explanation to the ubiquitous appearance of paretian probability laws in nature

approximation theorems for the propagators of higher order abstract cauchy problems in this paper we present two quite general approximation theorems for the propagators of higher order in time abstract cauchy problems which extend largely the classical trotter kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions then we apply the approximation theorems to deal with the second order dynamical boundary value problems

universality of accelerating change abstract on large time scales the progress of human technology follows an exponential growth trend that is termed accelerating change the exponential growth trend is commonly considered to be the amalgamated effect of consecutive technology revolutions where the progress carried in by each technology revolution follows an s curve and where the aging of each technology revolution drives humanity to push for the next technology revolution thus as a collective mankind is the intelligent designer of accelerating change in this paper we establish that the exponential growth trend and only this trend emerges universally on large time scales from systems that combine together two elements randomness and amalgamation hence the universal generation of accelerating change can be attained by systems with no intelligent designer

gini characterization of extreme value statistics abstract this paper presents a profound connection between gini s index and extreme value statistics gini s index is a quantitative gauge for the evenness of probability laws defined on the positive half line and is the common measure of societal egalitarianism applied in economics and in the social sciences extreme value statistics namely the gumbel frechet and weibull probability laws are the only possible asymptotic statistics emerging from the extremes of large ensembles of independent and identically distributed random variables extreme value statistics play a major role all across science and engineering in the analysis of rare and extreme events introducing generalizations of gini s index and exploring an elemental poissonian structure underlying the extreme value statistics we establish in this paper a gini based characterization of extreme value statistics

fractal poisson processes abstract the central limit theorem clt and extreme value theory evt study respectively the stochastic limit laws of sums and maxima of sequences of independent and identically distributed i i d random variables via an affine scaling scheme in this research we study the stochastic limit laws of populations of i i d random variables via nonlinear scaling schemes the stochastic population limits obtained are fractal poisson processes which are statistically self similar with respect to the scaling scheme applied and which are characterized by two elemental structures i a universal power law structure common to all limits and independent of the scaling scheme applied ii a specific structure contingent on the scaling scheme applied the sum projection and the maximum projection of the population limits obtained are generalizations of the classic clt and evt results extending them from affine to general nonlinear scaling schemes

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

identification of errors in variables systems with arma observation noises abstract the purpose of the paper is to give the recursive estimate for coefficients of the single input single output siso errors in variables eiv system and to prove its strong consistency the observation noises of the eiv system are assumed to be arma processes and the system input is taken to be an iid sequence the recursive estimation algorithm is given with the help of stochastic approximation sa method and the strong consistency is established under reasonable conditions the numerical simulation is consistent with the theoretical analysis

lindy s law abstract aging means that as things grow old their remaining expected lifetimes lessen either faster or slower most of the things we encounter in our everyday lives age with time however there are things that do quite the opposite they anti age as they grow old their remaining expected lifetimes increase rather than decrease a quantitative formulation of anti aging is given by the so called lindy s law in this paper we explore lindy s law and its connections to pareto s law to zipf s law and to socioeconomic inequality

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

dynamic errors in variables systems with three variables abstract errors in variables problems are considered for the case of three variables where the underlying relations among the noise free variables are linear and covariance information for the noisy variables is available the static problem where the variables are complex which can arise when narrowband filtering is used is analysed in detail some results are also presented for the case when the linear relations among the variables are defined by dynamic transfer functions

fractal probability laws we explore six classes of fractal probability laws defined on the positive half line weibull frechet levy hyper pareto hyper beta and hyper shot noise each of these classes admits a unique statistical power law structure and is uniquely associated with a certain operation of renormalization all six classes turn out to be one dimensional projections of underlying poisson processes which in turn are the unique fixed points of poissonian renormalizations the first three classes correspond to linear poissonian renormalizations and are intimately related to extreme value theory weibull frechet and to the central limit theorem levy the other three classes correspond to nonlinear poissonian renormalizations pareto s law commonly perceived as the universal fractal probability distribution is merely a special case of the hyper pareto class

on nonlinear wave equations of carrier type abstract this paper is concerned with the initial boundary value problem of the n dimensional carrier equation with an internal damping this damping is a fractional power of the velocity of the points of the material the faedo galerkin method tartar approach and compactness arguments provide the global existence of solutions of the above problem with restriction on the size of the initial data the decay of solutions is obtained by the perturbation method

existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions abstract in this paper we consider a multi dimensional damped semilinear viscoelastic wave equation with variable coefficient and acoustic boundary conditions first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem second we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time and we prove the uniform decay rate of the energy

benford s law a poisson perspective abstract benford s law is a counterintuitive statistical law asserting that the distribution of leading digits taken from a large ensemble of positive numerical values that range over many orders of scale is logarithmic rather than uniform as intuition suggests in this paper we explore benford s law from a poisson perspective considering ensembles of positive numerical values governed by poisson process statistics we show that this poisson setting naturally accommodates benford s law and i establish a poisson characterization and a poisson multidigit extension of benford s law ii study a system invariant leading digit distribution which generalizes benford s law and establish a poisson characterization and a poisson multidigit extension of this distribution iii explore the universal emergence of the system invariant leading digit distribution couple this universal emergence to the universal emergence of the weibull and frechet extreme value distributions and distinguish the special role of benford s law in this universal emergence iv study the continued fractions counterpart of the system invariant leading digit distribution and establish a poisson characterization of this distribution and v unveil the elemental connection between the system invariant leading digit distribution and its continued fractions counterpart this paper presents a panoramic poisson approach to benford s law to its system invariant generalization and to its continued fractions counterpart

paretian poisson processes many random populations can be modeled as a countable set of points scattered randomly on the positive half line the points may represent magnitudes of earthquakes and tornados masses of stars market values of public companies etc in this article we explore a specific class of random such populations we coin paretian poisson processes this class is elemental in statistical physics connecting together in a deep and fundamental way diverse issues including the poisson distribution of the law of small numbers paretian tail statistics the frechet distribution of extreme value theory the one sided levy distribution of the central limit theorem scale invariance renormalization and fractality resilience to random perturbations

identification of dynamic errors in variables models this paper deals with the identifiability of scalar dynamic errors in variables models characterized by rational spectra the hypothesis of causality for the underlying dynamic system is taken into account by making use of stochastic realization theory and of the structural properties of state space representations it is shown that under mild assumptions the model is uniquely identified

measuring statistical heterogeneity the pietra index abstract there are various ways of quantifying the statistical heterogeneity of a given probability law statistics uses variance which measures the law s dispersion around its mean physics and information theory use entropy which measures the law s randomness economics uses the gini index which measures the law s egalitarianism in this research we explore an alternative to the gini index the pietra index which is a counterpart of the kolmogorov smirnov statistic the pietra index is shown to be a natural and elemental measure of statistical heterogeneity which is especially useful in the case of asymmetric and skewed probability laws and in the case of asymptotically paretian laws with finite mean and infinite variance moreover the pietra index is shown to have immediate and fundamental interpretations within the following applications renewal processes and continuous time random walks infinite server queueing systems and shot noise processes financial derivatives the interpretation of the pietra index within the context of financial derivatives implies that derivative markets in effect use the pietra index as their benchmark measure of statistical heterogeneity

decay rate estimates for wave equations of memory type with acoustic boundary conditions abstract a wave equation of memory type u u 0 t g t s u s d s 0 with acoustic boundary conditions is considered this work is devoted to investigating the influence of the kernel function g and proving general rates of decay of solutions when g does not necessarily decay exponentially

measuring statistical evenness a panoramic overview motivated by the question how equal is the distribution of wealth within a given human population economics devised an impressive toolbox of quantitative measures of societal egalitarianism including the lorenz curve and the following indices gini pietra hoover amato hirschman theil and atkinson these quantitative measures considered in the broader context of general data sets with positive values are in effect general gauges of statistical evenness while the application of gini s index grew beyond economics and reached diverse fields of science the aforementioned evenness toolbox has largely remained within the confines of the social sciences the aim of this paper is to expose this evenness toolbox to the physics community by presenting a comprehensive evenness based approach to a fundamental problem in science the measurement of statistical heterogeneity

on a mixed problem with a nonlinear acoustic boundary condition for a non locally reacting boundaries abstract we discuss global solvability to the mixed problem for a nonlinear wave equation in domains with non locally reacting boundaries and nonlinear acoustic boundary condition we prove the existence and uniqueness of solution additionally using the method of nakao we demonstrate the decay of the associated energy stability

the distribution of first passage times and durations in forex and future markets abstract possible distributions are discussed for intertrade durations and first passage processes in financial markets the view point of renewal theory is assumed in order to represent market data with relatively long durations two types of distributions are used namely a distribution derived from the mittag leffler survival function and the weibull distribution for the mittag leffler type distribution the average waiting time residual life time is strongly dependent on the choice of a cut off parameter t max whereas the results based on the weibull distribution do not depend on such a cut off therefore a weibull distribution is more convenient than a mittag leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations on the other hand we find that the gini index is rather independent of the cut off parameter based on the above considerations we propose a good candidate for describing the distribution of first passage time in a market the weibull distribution with a power law tail this distribution compensates the gap between theoretical and empirical results more efficiently than a simple weibull distribution it should be stressed that a weibull distribution with a power law tail is more flexible than the mittag leffler distribution which itself can be approximated by a weibull distribution and a power law indeed the key point is that in the former case there is freedom of choice for the exponent of the power law attached to the weibull distribution which can exceed 1 in order to reproduce decays faster than possible with a mittag leffler distribution we also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory moreover we discuss the limitation of our distributions by applying our distribution to the analysis of the btp future and calculating the average waiting time we find that our distribution is applicable as long as durations follow a weibull law for short times and do not have too heavy a tail

chaotic dynamics markov partitions and zipf s law a chaotic dynamics model creating markovian strings of symbols as well as sequences of words is presented and its possible relevance to zipf s law is discussed

brownian gas models for extreme value laws in this paper we establish one dimensional brownian gas models for the extreme value laws of gumbel weibull and frechet a gas model is a countable collection of independent particles governed by common diffusion dynamics the extreme value laws are the universal probability distributions governing the affine scaling limits of the maxima and minima of ensembles of independent and identically distributed one dimensional random variables using the recently introduced concept of stationary poissonian intensities we construct two gas models whose global statistical structures are stationary and yield the extreme value laws a linear brownian motion gas model for the gumbel law and a geometric brownian motion gas model for the weibull and frechet laws the stochastic dynamics of these gas models are studied in detail and closed form analytical descriptions of their temporal correlation structures their topological phase transitions and their intrinsic first passage time fluxes are presented

the abstract cauchy problem for dissipative operators with respect to metric like functionals abstract this paper is devoted to a characterization of semigroups of lipschitz operators on a closed subset d of a banach space x and the abstract cauchy problem for an operator a in x satisfying the following condition there exists a proper lower semicontinuous functional from x into 0 such that the effective domain of is d a and such that lim n a x n a x in x for any x d a and any sequence x n in d a satisfying two conditions lim n x n x in x and lim sup n x n x the main result asserts that a semigroup of lipschitz operators on d can be generated by an operator a satisfying the above mentioned condition a dissipative condition with respect to a metric like functional and a subtangential condition the kirchhoff equations with acoustic boundary conditions are solved by the method based on the abstract result with the construction of suitable liapunov functionals and the use of a metric like functional on a suitable set

identification methods in a unified framework the paper derives a framework suitable to discuss the classical koopmans levin kl and maximum likelihood ml algorithms to estimate parameters of errors in variables linear models in a unified way using the capability of the unified approach a new parameter estimation algorithm is presented offering flexibility to ensure acceptable variance in the estimated parameters the developed algorithm is based on the application of hankel matrices of variable size and can equally be considered as a generalized version of the kl method gkl or as a reduced version of the ml estimation the methodology applied to derive the gkl algorithm is used to present a straightforward derivation of the subspace identification algorithm

an application of semigroups of locally lipschitz operators to carrier equations with acoustic boundary conditions abstract a generation theorem of semigroups of locally lipschitz operators on a subset of a real banach space is given and applied to the problem of the well posedness of the carrier equation u t t u 2 u u t p 1 u t 0 in 0 with acoustic boundary condition where p 2 and is a bounded domain in an arbitrary dimensional space

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

polynomial stability for wave equations with acoustic boundary conditions and boundary memory damping we study wave equations with acoustic boundary conditions where only one memory damping acts on the acoustic boundary under some conditions on the memory kernel polynomial energy decay rates are established by using higher order energy estimates among some other techniques

well posedness for a variable coefficient wave equation with nonlinear damped acoustic boundary conditions abstract we consider a variable coefficient wave equation with nonlinear damped acoustic boundary conditions well posedness in the hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups

fluctuations in time intervals of financial data from the view point of the gini index abstract we propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the gini index we show the explicit form of the gini index for a weibull distribution a good candidate to describe the first passage time of foreign exchange rate the analytical expression of the gini index compares well with the value obtained from empirical data

brief paper recursive identification for multivariate errors in variables systems the recursive algorithm is given for estimating matrix coefficients of the multivariate errors in variables eiv systems it is shown that under mild conditions the estimate given by the algorithm converges to a limit belonging to the solution set of the yule walker equation satisfied by the true coefficients of the system the sufficient conditions guaranteeing the uniqueness of the solution to the yule walker equation are given in this case the estimate provided by the recursive algorithm is strongly consistent

asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions abstract in this paper we consider a multi dimensional wave equation with dynamic boundary conditions related to the kelvin voigt damping global existence and asymptotic stability of solutions starting in a stable set are proved blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained

linear dynamic errors in variables models some structure theory abstract this paper gives a survey of some recent results on problems of identifiability or more general of the relation between the observations and certain system characteristics for linear dynamic errors in variables models for a large part of the paper the noise components are assumed to be mutually uncorrelated after the general problem statement a rather complete analysis of the single input single output case is given also the case of three variables and the case where the number of inputs is equal to the number of outputs are discussed in detail finally the use of higher order cummulant spectra for identifiability is investigated

zipf law an extreme perspective extreme value theory evt asserts that the frechet law emerges universally from linearly scaled maxima of collections of independent and identically distributed random variables that are positive valued observations of many real world sizes e g city sizes give rise to the zipf law if we rank the sizes decreasingly and plot the log sizes versus the log ranks then an affine line emerges in this paper we present an evt approach to the zipf law specifically we establish that whenever the frechet law emerges from the evt setting then the zipf law follows the evt generation of the zipf law its universality and its associated phase transition are analyzed and described in detail

an improved bias compensation approach for errors in variables model identification parametric estimation of the dynamic errors in variables models is considered in this paper in particular a bias compensation approach is examined in a generalized framework sufficient conditions for uniqueness of the identified model are presented subsequently a statistical accuracy analysis of the estimation algorithm is carried out the asymptotic covariance matrix of the system parameter estimates depends on a user chosen filter and a certain weighting matrix it is shown how these can be tuned to boost the estimation performance the numerical simulation results suggest that the covariance matrix of the estimated parameter vector is very close to the cramer rao lower bound for the estimation problem

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

paper identification of scalar errors in variables models with dynamics the paper considers the task of identifying a causal linear dynamic system excited by stationary gaussian zero mean noise of unknown spectrum and given measurements of the system input and output contaminated by independent additive stationary noise signals of unknown spectra while the solution is normally not unique finite dimensional parameterizations of the solution set are given in some cases involving just one parameter even though the various spectra may not be rational

complete second order differential equations in banach spaces with dynamic boundary conditions abstract in this paper we deal with the mixed initial boundary value problem for complete second order in time linear differential equations in banach spaces in which time derivatives occur in the boundary conditions general wellposedness theorems are obtained for the first time which are used to solve the corresponding inhomogeneous problems examples of applications to initial boundary value problems for partial differential equations are also presented

gini estimation under infinite variance we study the problems related to the estimation of the gini index in presence of a fat tailed data generating process i e one in the stable distribution class with finite mean but infinite variance i e with tail index 1 2 we show that in such a case the gini coefficient cannot be reliably estimated using conventional nonparametric methods because of a downward bias that emerges under fat tails this has important implications for the ongoing discussion about economic inequality we start by discussing how the nonparametric estimator of the gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution as the data distribution shifts from the domain of attraction of a light tailed distribution to that of a fat tailed one especially in the case of infinite variance we also show how the nonparametric gini bias increases with lower values of we then prove that maximum likelihood estimation outperforms nonparametric methods requiring a much smaller sample size to reach efficiency finally for fat tailed data we provide a simple correction mechanism to the small sample bias of the nonparametric estimator based on the distance between the mode and the mean of its asymptotic distribution

identification of linear relations from noisy data geometrical aspects abstract the problem of determining linear models from data corrupted by noise has been revisited by several authors in recent years with reference to the frisch scheme this work presents some geometrical aspects regarding the sets of solutions obtained in the identification procedure an analysis is made on how these sets vary as the amount of noise on the data varies the existence of particular solutions for data linked by a number of linear relations greater than one is also shown

diversity of poissonian populations populations represented by collections of points scattered randomly on the real line are ubiquitous in science and engineering the statistical modeling of such populations leads naturally to poissonian populations poisson processes on the real line with a distinguished maximal point poissonian populations are infinite objects underlying key issues in statistical physics probability theory and random fractals due to their infiniteness measuring the diversity of poissonian populations depends on the lower bound cut off applied this research characterizes the classes of poissonian populations whose diversities are invariant with respect to the cut off level applied and establishes an elemental connection between these classes and extreme value theory the measures of diversity considered are variance and dispersion simpson s index and inverse participation ratio shannon s entropy and renyi s entropy and gini s index

universal poisson process limits for general random walks abstract this paper considers ensembles of general independent and identically distributed random walks taking the ensemble size to grow infinitely large and also taking the running time of the random walks to grow infinitely large universal poisson process limits are obtained specifically it is established that the positions of general linear random walks converge universally to poisson processes over the real line with uniform and exponential intensities and it is established that the positions of general geometric random walks converge universally to poisson processes over the positive half line with harmonic and power intensities corollaries to these universal convergence results yield the extreme value statistics of gumbel weibull and frechet

brief identification of nonlinear errors in variables models a new identification algorithm for nonlinear but linear in parameters errors in variables models is presented using nonlinear polynomial eigenvalue eigenvector decompositions

identification of multivariable dynamic errors in variables system with arbitrary inputs the present work deals with the identification of multivariable linear dynamic system from noisy input output observations where the input signal is arbitrary and the input output noises are mutually correlated a frequency domain identification framework is developed in which the consistent estimator of the multivariable plant model parameters and of the input output noise covariance matrix is defined as the solution of a set of normal equations and sufficient conditions for the uniqueness of the parameter estimate are established based on the rank property of the matrix of the normal equation the uncertainty bound of the parameter estimates is constructed and compared with the cramer rao lower bound the proposed methodology is validated on a simulated multivariable dynamic system

errors in variables identification of dynamic systems excited by arbitrary non white input abstract this work deals with the identification of dynamic systems from noisy input output observations where the noise free input is not parameterized the basic assumptions made are 1 the dynamic system can be modeled by a discrete or continuous time rational transfer function model 2 the temporal input output disturbances are mutually independent identically distributed noises and 3 the input power spectrum is non white not necessarily rational and is modeled nonparametrically the system identifiability is guaranteed by exploiting the non white spectrum property of the noise free input a frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input output noise variances the uncertainty bound of the estimates is calculated and compared to the cramer rao lower bound the efficiency of the proposed algorithm is illustrated on numerical examples

nonparametric identification of linear dynamic errors in variables systems the present work handles the nonparametric identification of linear dynamic systems within an errors in variables framework where the input is arbitrary and both the input and output disturbing noises are white with unknown variances using the property that the frequency response function and the system leakage term can be locally approximated very well by a low order degree polynomial a frequency domain estimator is developed which gives consistent estimates for the frequency response function and the input output noise variances the consistency and uniqueness of the estimator are theoretically analyzed under mild conditions and uncertainty bounds are also provided the proposed method is finally validated on a simulated linear dynamic system