passive stochastic approximation with constant step size and window width motivated by the desire to solve a steady state estimation and detection problem in chemical engineering and inspired by the recent progress in passive stochastic approximation recursive algorithms combining stochastic approximation and kernel estimation are studied and developed in this work the underlying problem can be stated as finding the roots f x 0 provided only noisy measurements y sub n f x sub n spl xi sub n are available where ef x spl xi sub n f x the main difficulty lies in that unlike the traditional approach in stochastic approximation the sequence x sub n is generated randomly and cannot be adjusted in accordance with our wish similar to those used in the decreasing step size algorithms another sequence z sub n is generated to approximate the roots of f x 0 some of the features of the algorithms include constant step size and constant window width and correlated random processes under fairly general conditions it is proven that a weak convergence result holds for an interpolated sequence of the iterates error bounds are obtained and a local limit theorem is also derived the algorithm is then applied to an estimation problem in chemical engineering simulation has shown promising results

adaptive lexicographic optimization in multi class m gi 1 queues we consider a multi class m gi 1 system in which an average response time objective is associated with each class the performance of each class is measured by the ratio of the average response time over the corresponding value of the objective to achieve fairness in service allocation it is required to find a policy that lexicographically minimizes the vector of performance ratios arranged in nonincreasing order we provide such a policy that is adaptive uses only knowledge of arrival and departure instants and is thus easy to implement we also consider a variant of this policy which adapts faster to changes in the statistical parameters of the model both policies are analyzed via associated stochastic recursions using techniques of stochastic approximation

improved stable approximants using the routh array a simple method for obtaining a stable reduced order k th order approximant g k s for a stable hlgh order n th order transfer function g s is described the method is an improvement over some previous methods 1 2 in that it not only ensures matching of the first k time moments of g s and g k s but it also ensures that the k 1 th time moment of g k s be as close as possible to the corresponding value in g s

deviation inequalities for random walks we study random walks on groups with the feature that roughly speaking successive positions of the walk tend to be aligned we formalize and quantify this property by means of the notion of deviation inequalities we show that deviation inequalities have several consequences including central limit theorems the local lipschitz continuity of the rate of escape and entropy as well as linear upper and lower bounds on the variance of the distance of the position of the walk from its initial point in the second part of this article we show that the exponential deviation inequality holds for measures with exponential tail on acylindrically hyperbolic groups these include nonelementary relatively hyperbolic groups mapping class groups many groups acting on cat 0 spaces and small cancellation groups

improvements in the application of stochastic estimation algorithms parameter jump detection the paper discusses the problem of recursive algorithms for estimating parameters which are subject to random jumps a new method is presented which consists of detecting these parameter jumps and should a detection occur reinitializing the estimation gain sequence new variables required by this method are calculated by means of diffusion approximations some simulation results illustrate the improved adaptation capabilities offered by the method

tracking characteristics of an obe parameter estimation algorithm the tracking properties of a recursive parameter bounding algorithm referred to as the dasgupta huang optimal bounding ellipsoid algorithm dhobe algorithm are investigated conditions that ensure the existence of these 100 confidence regions in the face of small model parameter variations are derived for larger parameter variations it is shown that the existence of 100 confidence regions is guaranteed asymptotically a modification that enables the algorithm to track large variations in model parameter is proposed simulation results show that in general the modified algorithm has a tracking performance comparable and in some cases superior to that of the exponentially weighted recursive least squares rls algorithm

heat kernel estimates and riesz transforms on some riemannian covering manifolds consider a riemannian manifold m which is a galois covering of a compact manifold with nilpotent deck transformation group g for the laplace operator on m we prove a precise estimate for the gradient of the heat kernel and show that the riesz transforms are bounded in l p m 1 p we also obtain estimates for discrete oscillations of the heat kernel and boundedness of discrete riesz transform operators which are defined using the action of g on m

multilayer neural networks for reduced rank approximation this paper is developed in two parts first the authors formulate the solution to the general reduced rank linear approximation problem relaxing the invertibility assumption of the input autocorrelation matrix used by previous authors the authors treatment unifies linear regression wiener filtering full rank approximation auto association networks svd and principal component analysis pca as special cases the authors analysis also shows that two layer linear neural networks with reduced number of hidden units trained with the least squares error criterion produce weights that correspond to the generalized singular value decomposition of the input teacher cross correlation matrix and the input data matrix as a corollary the linear two layer backpropagation model with reduced hidden layer extracts an arbitrary linear combination of the generalized singular vector components second the authors investigate artificial neural network models for the solution of the related generalized eigenvalue problem by introducing and utilizing the extended concept of deflation originally proposed for the standard eigenvalue problem the authors are able to find that a sequential version of linear bp can extract the exact generalized eigenvector components the advantage of this approach is that it s easier to update the model structure by adding one more unit or pruning one or more units when the application requires it an alternative approach for extracting the exact components is to use a set of lateral connections among the hidden units trained in such a way as to enforce orthogonality among the upper and lower layer weights the authors call this the lateral orthogonalization network lon and show via theoretical analysis and verify via simulation that the network extracts the desired components the advantage of the lon based model is that it can be applied in a parallel fashion so that the components are extracted concurrently finally the authors show the application of their results to the solution of the identification problem of systems whose excitation has a non invertible autocorrelation matrix previous identification methods usually rely on the invertibility assumption of the input autocorrelation therefore they can not be applied to this case

polynomial growth harmonic functions on groups of polynomial volume growth we consider harmonic functions of polynomial growth of some order d on cayley graphs of discrete groups of polynomial volume growth of order d w r t the word metric and prove the optimal estimate for the dimension of the space of such harmonic functions more precisely the dimension of this space of harmonic functions is at most of order d d 1 as in the already known riemannian case this estimate is polynomial in the growth degree more generally our techniques also apply to graphs roughly isometric to cayley graphs of groups of polynomial volume growth

a measure of the tracking capability of recursive stochastic algorithms with constant gains a criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time varying systems the optimal gain for a given disturbance is also calculated this criterion is seen to have some connection with the fisher information matrix and allows us to select a priori the best algorithm for identifying a given unknown parameter which may be subject to smooth unknown disturbances examples of applications are given in the areas of identification theory and data communication theory

on drift and entropy growth for random walks on groups in this paper we consider drift and entropy growth for symmetric finitary random walks on finitely generated groups we construct examples of various intermediate asymptotics of the drift for such random walks we establish general inequalities which connect drift entropy and exponential growth rate of groups then we apply these inequalities to get estimates for entropy in particular examples

random walks on discrete groups of polynomial volume growth let mu be a probability measure with finite support on a discrete group gamma of polynomial volume growth the main purpose of this paper is to study the asymptotic behavior of the convolution powers mu n of mu if mu is centered then we prove upper and lower gaussian estimates we prove a central limit theorem and we give a generalization of the berry esseen theorem these results also extend to noncentered probability measures we study the associated riesz transform operators the main tool is a parabolic harnack inequality for centered probability measures which is proved by using ideas from homogenization theory and by adapting the method of krylov and safonov this inequality implies that the positive mu harmonic functions are constant finally we give a characterization of the mu harmonic functions which grow polynomially

paper tracking error bounds of adaptive nonstationary filtering adaptive filtering with error gradient algorithm and constant step size is analyzed for a deterministic time variable optimum filtering vector the unrealistic assumption of independent observations is replaced by a bounded memory model largely justifiable in applications then the mean square tracking deviation msd between the optimum vector and the algorithm output is proved to include two contributions the stationary mode error characteristic of convergence accuracy which is proportional to the step size and the transient mode error reflecting the rapidity of tracking which is proportional to the squared ratio of the maximum optimum estimator increment to the step size this result agrees with the common intuition that there exists an optimum step size which compromises between convergence accuracy and tracking speed

tracking analysis of an arma parameter estimation algorithm the problem of adaptively estimating parameters of a time varying autoregressive moving average arma process using a constant step size gauss newton algorithm is studied using weak convergence theory and the concept of prescaling it is shown that an ordinary differential equation can be used to describe the mean behavior of the adaptive filter coefficients computer simulations are provided to substantiate the analysis

the error variance of lms with time varying weights a calculation of weight error variance of the lms least mean square algorithm is made in the presence of time varying true weights with time varying weights the lms error system has in general several time scales operating at once this causes difficulties in the variance calculation which seem hitherto to have passed unnoticed to handle this problem a sort of perturbation expansion is developed based on weak convergence methods or stochastic averaging the main concern in carrying out the error variance calculation is to study the effect on lms performance of adaptation speed as it relates to true speed of parameter change three cases are covered with reference to considering adaptation speed with respect to true speed first where the adaptation speed is too slow second where it is matched and third where it is faster

tracking analysis of the sign algorithm in nonstationary environments a tracking analysis of the adaptive filters equipped with the sign algorithm and operating in nonstationary environments is presented under the assumption that the nonstationary can be modeled using a random disturbance it is shown that the long term time average of the mean absolute error is bounded and that there exists an optimal choice of the convergence constant mu which minimizes this quality applying the commonly used independence assumption and under the assumption that the nonstationarity is solely due to the time varying behavior of the optimal coefficients it is shown that the distributions of the successive coefficient misalignment vectors converge to a limiting distribution when the adaptive filter is used in the system identification mode finally under the additional assumption that the signals involved are zero mean and gaussian a set of nonlinear difference equations is derived that characterizes the mean and mean squared behavior of the filter coefficients and the mean squared estimation error during adaptation and tracking results of several experiments that show very good correlation with the theoretical analyses are presented

local limit theorem for symmetric random walks in gromov hyperbolic groups completing a strategy of gouezel and lalley we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non elementary gromov hyperbolic group denoting by r the inverse of the spectral radius of the random walk the probability to return to the identity at time n behaves like c r n n 3 2 an important step in the proof is to extend ancona s results on the martin boundary up to the spectral radius we show that the martin boundary for r harmonic functions coincides with the geometric boundary of the group in an appendix we explain how the symmetry assumption of the measure can be dispensed with for surface groups

nonasymptotic results for finite memory wls filters a nonasymptotic analysis of properties of weighted least squares wls adaptive filters used for identification of time varying systems is presented it is shown that the problem of mean square boundedness of wls estimates is closely related to the problem of invertibility in the mean sense of the corresponding regression matrix necessary and sufficient conditions are discussed for such invertibility to hold based on that a number of results are derived paralleling those already obtained for least mean square lms filters and the problem of statistical robustness of the wls estimator is briefly discussed

the limiting behavior of lms a realization oriented analysis is given of the gradient noise misadjustment and lag misadjustment performance of the lms least mean square algorithm new formulas are given for both of these components of excess mean square error it is shown that the traditional formula for lag misadjustment needs to be modified by adding further terms due to gradient noise and noise variance to perform the analysis it is necessary to study the convergence with probability one of the noise free fixed parameter lms algorithm convergence is found under simple conditions that improve on those previously obtained

identification of nonstationary stochastic systems using parallel estimation schemes the parallel multiple model schemes for identification of nonstationary stochastic systems are considered first the form of the optimal local bayesian predictor is derived under the assumptions that system coefficients vary according to the random walk model and that the kalman filter based algorithms are used for identification purposes a rational extension of this strategy which can be applied to identification algorithms of any form is discussed specific suggestions are made concerning the possible choice of adaptation gains of the competitive adaptive filters computer simulation results confirming the good estimation robustness properties of the parallel identification schemes are presented it is shown that the proposed scheme can significantly decrease sensitivity of the identification algorithm to the rate of nonstationarity of the analyzed system or alternatively to the choice of design parameters such as adaptation gains and forgetting factors

uncertainties for recursive estimators in nonlinear state space models with applications to epidemiology consider a nonlinear dynamic system where one wishes to estimate a state vector using noisy measurements many algorithms have been proposed to address this problem among them the extended kalman filter and its variants and constant gain stochastic approximation to quantify the efficacy of these algorithms it is necessary to describe the distribution of the state estimation error typically performance has been measured by the estimation error covariance alone which does not provide enough information to probabilistically quantify the estimation accuracy by casting the estimation error in an autoregressive type form this paper addresses the broader question of the distribution of the error for a general class of recursive algorithms we illustrate the distributional results in an epidemiological problem of disease monitoring

a note on the model reduction problem a mixed method of model reduction is proposed it is based on the differentiation method suggested by gutman et al 1 and on the usual pade method more precisely the differentiation procedure is used to obtain the reduced order denominator thus ensuring stability preservation while the numerator is obtained by matching the first maclaurin expansion coefficients of the original system and model transfer functions the method is computationally very simple and may lead to satisfactory results as shown by an example where the original system transfer function is taken from the relevant literature

tracking characteristics of the constrained iir adaptive notch filter the tracking behavior of a constrained iir notch filter the coefficients of which are estimated using a constant step size gauss newton algorithm is studied using weak convergence theory and the concept of prescaling it is shown that the mean behavior of the adaptive filter coefficients can be studied by using an ordinary differential equation ode approximate and simple closed form results are derived for the tracking behavior of a second order notch filter computer simulations are presented to substantiate the analysis

on the asymptotic accuracy of pseudo linear regression algorithms the accuracy properties of a general pseudo linear regression plr method are examined both off line and on line algorithms are considered assuming the parameter estimates converge they will under weak conditions be asymptotically gaussian distributed expressions for the corresponding covariance matrices are given it is shown that the asymptotic covariance matrix of the off line plr algorithm is bounded from above by the matrix corresponding to the on line plr algorithm and from below by that corresponding to the prediction error method some simple numerical illustrations of the theoretical results are also included

discrete time model reference adaptive control for continuous time systems using generalized sampled data hold functions the generalized sampled data hold functions approach of p t kabamba 1987 is extended to the control of linear time invariant systems with unknown parameters the idea of kabamba s approach is to periodically sample the plant output and define the control as the sampled output plus a discrete time reference each multiplied by an individual modulating function such a control makes it possible to assign an arbitrary discrete time transfer function for the sampled closed loop system and does not make assumptions on the plant other than controllability and observability the authors propose an indirect adaptive controller which is based on this approach and estimates the modulating functions online in particular the control is modified so that persistent excitation of the continuous time plant is ensured without making an assumption on the reference signal and discrete time asymptotic model following is nevertheless obtained the only assumptions on the plant are minimality for the continuous and sampled plant and known order

application of benveniste s convergence results in the study of adaptive iir filtering algorithms it is shown that the weak convergence results of a benveniste et al ieee trans automat contr vol ac 25 p 1042 58 dec 1980 can be used to prove convergence of some adaptive infinite impulse response iir filtering algorithms the association of the algorithms with some ordinary differential equations for constant gains which parallels the theory of l ljung et al 1983 is suitable for constant gain adaptive filtering applications convergence proofs for a prefiltering algorithm for a simple constant gain version of the recursive maximum likelihood algorithm and for the well known simple hyperstable adaptive recursive filter sharf algorithm are given as examples

boundary and entropy of space homogeneous markov chains we study the poisson boundary equiv representation of bounded harmonic functions of markov operators on discrete state spaces that are invariant under the action of a transitive group of permutations this automorphism group is locally compact but not necessarily discrete or unimodular the main technical tool is the entropy theory which we develop along the same lines as in the case of random walks on countable groups while however the implementation is different and exploits discreteness of the state space on the one hand and the path space of the induced random walk on the nondiscrete group on the other various new examples are given as applications including a description of the poisson boundary for random walks on vertex transitive graphs with infinitely many ends and on the diestel leader graphs

first order tracking properties of weighted least squares estimators the first order tracking properties evolution of the mean tracking error of weighted least squares wls estimators applied to nonstationary system identification are investigated the expected path of the parameter estimates is evaluated the concept of the impulse response associated with the wls estimator is introduced

asymptotic entropy of random walks on fuchsian buildings and kac moody groups in this article we prove existence of the asymptotic entropy for isotropic random walks on regular fuchsian buildings moreover we give formulae for the asymptotic entropy and prove that it is equal to the rate of escape of the random walk with respect to the green distance when the building arises from a fuchsian kac moody group our results imply results for random walks induced by bi invariant measures on these groups however our results are proven in the general setting without the assumption of any group acting on the building the main idea is to consider the retraction of the isotropic random walk onto an apartment of the building to prove existence of the asymptotic entropy for this retracted walk and to lift this in order to deduce the existence of the entropy for the random walk on the building

ar and arma identification algorithms of levinson type an innovations approach fast recursive in time identification procedures for both ar and arma processes e g chandrasekhar square root algorithms have been available for a few years these algorithms realize the desired transfer functions in the classical polynomial or rational form on the other hand the synthesis of polynomial and rational transfer functions in lattice and ladder form has fostered great interest in network theory by virtue of its pleasant properties this type of synthesis is strongly related to the theory of orthogonal polynomials on the unit circle an identification procedure with the realization of the desired whitening filter in lattice form was available for ar processes we give here a simple approach for obtaining such algorithms investigating furthermore the connections between the so obtained algorithms and the classical ones least squares procedure in the same way we obtain identification procedures with realization of the desired filter in lattice and ladder form for arma processes together with the connection with the classical extended least squares procedure the method is based upon a fairly general levinson orthogonalization lemma in hilbert space involving innovation techniques we extend the method to various other estimation problems the algorithms we obtain are fast even somewhat faster than the previous fast ones and seem to be well conditioned

internal diffusion limited aggregation on discrete groups having exponential growth the internal diffusion limited aggregation dla has been introduced by diaconis and fulton rend sem mat univ pol torino 49 95 119 1991 it is a growth model defined on an infinite set and associated to a markov chain on this set we focus here on sets which are finitely generated groups with exponential growth we prove a shape theorem for the internal dla on such groups associated to symmetric random walks for that purpose we introduce a new distance associated to the green function which happens to have some interesting properties in the case of homogeneous trees we also get the right order for the fluctuations of that model around its limiting shape

behaviour of the output error identification algorithm for small stepsize gains in the output error identification algorithm it is possible to adjust a gain parameter to trade off for example sensitivity to noise and capacity to track plant parameter variations the rate of convergence of the ideal algorithm obtained in the noise free time invariant plant parameter case is related to the magnitude of this gain parameter the analysis applies to a broader class of adaptive problems than output error identification and in particular a positive real transfer function appearing in the problem formulation is allowed to be nonrational an alternative to the usual lyapunov based analysis is then needed

identification of certain time varying nonlinear wiener and hammerstein systems the problem of identification and tracking of time varying nonlinear systems is addressed in particular the wiener system that consists of a dynamic time varying linear part followed by a fixed nonlinearity and the hammerstein system in which the order of these two blocks is reversed are studied the extended kalman filter ekf algorithm is applied it is also shown that this algorithm can be reformulated in terms of a nonlinear minimization problem with a quadratic inequality constraint in order to ensure exponential stability resulting in the algorithm cekf as indicated by means of numerical examples this latter algorithm is less sensitive to the chosen initialization than the ekf the proposed algorithms depend on certain second order statistics that may be unknown in a typical scenario a method for estimation of these quantities is proposed it is demonstrated that the suggested algorithms can be successfully applied to the problem of acoustic echo cancelation

a structural view of asymptotic convergence speed of adaptive iir filtering algorithms i infinite precision implementation for pt i see ibid vol 41 no 4 p 1493 1517 1993 finite precision fp implementation is the ultimately inevitable reality of all adaptive filters including adaptive infinite impulse response iir filters this paper continues to examine the asymptotic convergence speed of adaptive iir filters of various structures and algorithms including the simple constant gain type and the newton type but under fp implementation a stochastic differential equation sde approach is used in the analysis such an approach not only greatly simplifies the fp analysis which is traditionally very involved algebraically but it also provides valuable information about the first order as well as the second order moments that the latter are not available using the ordinary differential equation ode approach the asymptotic convergence speed as well as the convergent values of the pertinent moments of fp errors are examined in terms of unknown system pole zero locations the adverse effects of lightly damped low frequency ldlf poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared the new results agree with the existing ones when reduced to the finite impulse response fir case in particular the explosive behavior of pertinent error variances of newton type iir algorithms when the forgetting factor spl lambda 1 is also concluded computer simulation verifies the predicted theoretical results

integral manifolds of slow adaptation conditions are given under which an integral manifold slow manifold exists for a nonlinear system representing a broad class of adaptive algorithms the parameter update equation restricted to the manifold is an exact description of the slow adaptation process which can be approximately analyzed by averaging stability properties of the slow motion in the manifold are extended off the manifold by a set of conditions under which the manifold is shown to be attractive this two time scale analysis provides a geometrical visualization of instability phenomena observed in adaptive systems and generalizes earlier local stability results

steady state and parameter tracking properties of self tuning minimum variance regulators abstract the self tuning regulator with a fixed gain and a fixed forgetting factor applied to control of an arx plant is considered the ordinary differential equation analysis of the closed loop system is performed in the neighbourhood of the stable equilibrium point and the approximate expressions for the steady state mean square parameter tracking and regulation errors are derived for the adaptive regulators based on the exponentially weighted least squares and stochastic approximation identification respectively it is shown that the concept of the effective memory length of the estimation algorithm has to be revised if the closed loop system identification with the gain fixing technique is used

riemannian geometric entropy for measuring network complexity a central issue in the science of complex systems is the quantitative characterization of complexity in the present work we address this issue by resorting to information geometry actually we propose a constructive way to associate with a in principle any network a differentiable object a riemannian manifold whose volume is used to define the entropy the effectiveness of the latter in measuring network complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale free networks as well as of characterizing small exponential random graphs configuration models and real networks

estimating time varying parameters by the kalman filter based algorithm stability and convergence convergence and stability properties of the kalman filter based parameter estimator are established for linear stochastic time varying regression models the main features are both the variances and sample path averages of the parameter tracking error are shown to be bounded the regression vector includes both stochastic and deterministic signals and no assumptions of stationarity or independence are requires and the unknown parameters are only assumed to have bounded variations in an average sense

optimization of adaptive identification for time varying filters adaptive identification in a time varying context is studied when controlled by the lms algorithm with constant gain under the assumption of correlated successive input vectors it is well known by experience that the tracking mean square error mse epsilon mu results from the tradeoff between the gradient part which is increasing and the lag contribution which is decreasing in this note we clarify the relative roles of the gradient and lag errors by proving their decoupled character this property relies upon independence between the additive noise at the output of the plant to be identified and the information vector at the plant input convergence of the mse is established rather than assumed quantitative evaluations of upper and lower bounds allow an approximate optimization of the gain in two important cases the optimum is exact one of these cases is slow variations it is defined in a quantitative manner thanks to the ratio of the variation noise to the output additive noise

on laws of large numbers for random walks we prove a general noncommutative law of large numbers this applies in particular to random walks on any locally finite homogeneous graph as well as to brownian motion on riemannian manifolds whi

the application of random reference sequences to the reconstruction of clipped differentiable signals the estimation of analog waveforms s t from their clipped contaminated samples is considered for differentiable signals s t appropriate estimates are established and their performance is investigated error bounds and convergence rates are derived which improve with the degree of differentiability of the signal s t the analytical results are supplemented by a simulation study

analysis on lie groups theorie locale diffusion de la chaleur sur des groupes de lie connexes la theorie globale les inegalites de sobolev bases graduees sur des corps lisses construction des bases graduees estimation locale du noyau diffusion de la chaleur demonstration de l inegalite de sobolev locale formes de dirichlet sur des groupes le semi groupe de convolution les conditions de sobolev modifiees

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

quantifying the effects of dimension on the convergence rate of the lms adaptive fir estimator the convergence rate of an lms adaptive fir filter to an unknown stationary channel may be influenced by the filter parameter dimension as well as by the input signal s characteristics this dimension influence may be of importance in applications such as adaptive acoustic echo cancellation in which the unknown channel is typically modeled as a long fir filter the paper includes the development and proposal of a novel measure of the expected convergence rate of the lms fir filter followed by analysis of this convergence rate measure the analysis indicates that unless the input signal is white the expected convergence rate decreases with increasing dimension down to a limiting value which is determined by the input signal s autocorrelation level

tree indexed random walks on groups and first passage percolation suppose that i i d random variables are attached to the edges of an infinite tree when the tree is large enough the partial sumss along some of its infinite paths will exhibit behavior atypical for an ordinary random walk this principle has appeared in works on branching random walks first passage percolation and rwre on trees we establish further quantitative versions of this principle which are applicable in these settings in particular different notions of speed for such a tree indexed walk correspond to different dimension notions for trees finally if the labeling variables take values in a group then properties of the group e g polynomial growth or a nontrivial poisson boundary are reflected in the sample path behavior of the resulting tree indexed walk

tracking algorithm designed by the local asymptotic approach the problem of sequential detection of parameter jumps in linear systems with constant noise level is discussed the detection problem is analyzed by the asymptotic local approach using the normalized output error sequence as the detection signal for linear regression armax and state space models a central limit theorem is proved transforming the original problem into the problem of detecting an increase in the man of an asymptotically gaussian distributed scalar process the performance of the tracking algorithm which consists of a parameter estimator with decreasing gain and a single hinkley s detector has been studied by simulations and compared to the performance of constant and adaptive gain parameter estimators the proposed algorithm seems to be superior in performance requiring only a little generally negligible additional computational effort the algorithm provides the information about the jump times and the time delay of jump detection seems to be unaffected by the measurement noise level provided that this level is not affected by the change

markov chain approximations to nonsymmetric diffusions with bounded coefficients we consider a certain class of nonsymmetric markov chains and obtain heat kernel bounds and parabolic harnack inequalities using the heat kernel estimates we establish a sufficient condition for the family of markov chains to converge to nonsymmetric diffusions as an application we approximate nonsymmetric diffusions in divergence form with bounded coefficients by nonsymmetric markov chains this extends the results by stroock and zheng to the nonsymmetric divergence forms 2012 wiley periodicals inc

the local limit theorem on nilpotent lie groups a local limit theorem is proven on connected simply connected nilpotent lie groups for a class of generating measures satisfying a moment condition and a condition on the characteristic function of the abelianization the result extends an earlier local limit theorem of alexopoulos which treated absolutely continuous measures with a continuous density of compact support and also extends local limit theorems of breuillard and diaconis hough which treated general measures on the heisenberg group

improved routh pade spl acute approximants a computer aided approach a geometric programming based computer aided method to derive a reduced order rth order approximant for a given stable siso linear continuous time system is presented in this method stability and the first r time moments markov parameters are preserved as well as the errors between a set of subsequent time moments markov parameters of the system and those of the model are minimized

filter order selection in adaptive maximum likelihood estimation the choice of the number of parameters is an important problem in adaptive filtering in the general ground of maximum likelihood ml parameter estimation akaike criterion has proved to be a very useful tool significant results and the importance of the kullback information measure as the implicit measure of distance associated with ml estimation are discussed application of these results to adaptive filtering is then considered for time invariant and time varying parametric models the corresponding practical forms of akaike criterion are given in the time varying case this criterion may be used as a way to fit the model into the nonstationarity of an exact filter the possible generalization of the akaike criterion to non ml estimation is discussed and application is made for weighted least squares estimation a more general approach to the nonstationary case is given by assuming a linear stochastic model for the vector of the filter coefficients in which case the ml estimate is computed recursively using the kalman filtering equation then the random sequence of kalman gains is close to a deterministic average sequence this sequence may be precomputed and gives an optimal choice for the gain matrices in an adaptive gradient type filter

centered densities on lie groups of polynomial volume growth we study the asymptotic behavior of the convolution powers of a centered density on a connected lie group g of polynomial volume growth the main tool is a harnack inequality which is proved by using ideas from homogenization theory and by adapting the method of krylov and safonov applying this inequality we prove that the positive harmonic functions are constant we also characterise the harmonic functions which grow polynomially we give gaussian estimates for as well as for the differences and we give estimates similar to the ones given by the classical berry esseen theorem for and we use these estimates to study the associated riesz transforms

analysis on nilpotent groups soit g un groupe de lie nilpotent reel simplement connexe et soit l son algebre de lie soient l 1 l et l k 1 l k l k 1 2 soit d d g d l k 1 kdim r l k l k 1 d est la dimension de dirichlet de g soit h un groupe nilpotent discret finiment genere on demontre des theoremes d analyse pour g

stable partial pade approximations for reduced order trnsfer functions while the pade approximation can often be used to produce good reduced order transfer functions the method suffers from the disadvantage that a stable reduced order model is not always obtained for an original model that is stable a method is described for obtaining stable partial pade approximation reduced order models the method permits the determination of the effect of changes in the coefficients in the partial pade approximation on the poles of the reduced order transfer function by means of standard root locus plots

when is adaptive better than optimal given a stationary process let us predict it using a first order predictor whose single coefficient is adapted to the current observations using a constant gain identification algorithm we investigate the prediction error variance as a function of the adaptation gain i e the length of the memory the number of observations of the identification scheme an infinite memory corresponds to the asymptotically constant optimal predictor and a finite memory to a locally adaptive time varying predictor we show that in some specified situations the prediction error variance associated with the finite memory adaptation scheme is smaller that the optimal variance this can only occur if the model is misspecified i e the structure of the optimal predictor is too simple

asymptotic entropy and green speed for random walks on countable groups we study asymptotic properties of the green metric associated with transient random walks on countable groups we prove that the rate of escape of the random walk computed in the green metric equals its asymptotic entropy the proof relies on integral representations of both quantities with the extended martin kernel in the case of finitely generated groups where this result is known benjamini and peres probab theory related fields 98 1994 91 112 we give an alternative proof relying on a version of the so called fundamental inequality relating the rate of escape the entropy and the logarithmic volume growth extended to random walks with unbounded support

catching homologies by geometric entropy abstract a geometric entropy is defined in terms of the riemannian volume of the parameter space of a statistical manifold associated with a given network as such it can be a good candidate for measuring networks complexity here we investigate its ability to single out topological features of networks proceeding in a bottom up manner first we consider small size networks by analytical methods and then large size networks by numerical techniques two different classes of networks the random graphs and the scale free networks are investigated computing their betti numbers and then showing the capability of geometric entropy of detecting homologies

frequency domain tracking characteristics of adaptive algorithms the problem of tracking time varying linear systems is discussed the focus is on the model quality in terms of the mean square error mse between the true momentary transfer function and the estimated one this mse is thus a function of frequency the exact expression for the mse is complicated but simple expressions that are asymptotic in the model order are developed for model structures of finite impulse response fir character simulations verify that these simple expressions are quite reliable and insightful even for moderate model orders expressions are developed for three basic adaptation algorithms recursive identification algorithms viz the least mean squares algorithm the recursive least squares algorithm with exponential forgetting and a tracking algorithm based on the kalman filter the results apply both to slowly time varying systems and to the model recovery after an abrupt change in the system dynamics

dimension free lp estimates for single riesz transforms via an h joint functional calculus abstract by using an h joint functional calculus for strongly commuting operators we derive a scheme to deduce the l p boundedness of certain d dimensional riesz transforms from the l p boundedness of appropriate one dimensional riesz transforms moreover the l p bounds we obtain are independent of the dimension the scheme is applied to riesz transforms connected with orthogonal expansions and discrete riesz transforms on products of groups with polynomial growth

bounded error identification of time varying parameters by rls techniques the performance of the recursive least squares algorithm with constant forgetting factor in the identification of time varying parameters is studied in a stochastic framework it is shown that the mean square tracking error keeps bounded if and only if the so called covariance matrix of the algorithm is l sup 1 bounded then a feasibility range for the forgetting factor is worked out in correspondence of which the covariance matrix and therefore the tracking error keeps bounded

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

on the convergence behavior of the lms and the normalized lms algorithms it is shown that the normalized least mean square nlms algorithm is a potentially faster converging algorithm compared to the lms algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics a very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the lms and nlms algorithms is proposed using this model answers can be obtained to questions for which no answers are currently available using other perhaps more realistic models examples are given to illustrate that even quantitatively the answers obtained can be good approximations it is emphasized that the convergence of the nlms algorithm can be speeded up significantly by employing a time varying step size the optimal step size sequence can be specified a priori for the case of a white input signal with arbitrary distribution

recursive parameter estimation for noisy autoregressive signals corresp the problem of recursively estimating the unknown parameters of a scalar autoregressive ar signal observed in additive white noise including signal power and noise variance is considered a state space model in a canonical but noninnovations form is used to represent the noisy ar signal an algorithm based on a system identification parameter estimation technique known as the recursive prediction error method is presented for recursive parameter estimation two simulation examples illustrate the effectiveness of the proposed algorithm

model free control of nonlinear stochastic systems with discrete time measurements consider the problem of developing a controller for general nonlinear and stochastic systems where the equations governing the system are unknown using discrete time measurement this paper presents an approach for estimating a controller without building or assuming a model for the system such an approach has potential advantages in accommodating complex systems with possibly time varying dynamics the controller is constructed through use of a function approximator such as a neural network or polynomial this paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements a convergence result for stochastic approximation algorithms with time varying objective functions and feedback is established it is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite difference gradient approximations

convergence rate determined for gradient based adaptive estimators abstract a convergence rate estimate is derived for the homogeneous gradient based adaptive linear estimator algorithm this estimate involves the eigenvalues of the regression vector covariance matrix yielding a useful measure for the choice of input signals for adaptive parameter estimation the connection between this criterion and those more familiar from nonadaptive system identification is made and comparisons are drawn between the two areas