extended stochastic gradient identification algorithms for hammerstein wiener armax systems an extended stochastic gradient algorithm is developed to estimate the parameters of hammerstein wiener armax models the basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates the obtained parameter estimates of the identification model include the product terms of the parameters of the original systems two methods of separating the parameter estimates of the original parameters from the product terms are discussed the average method and the singular value decomposition method to improve the identification accuracy an extended stochastic gradient algorithm with a forgetting factor is presented the simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor

brief paper least squares based iterative identification for a class of multirate systems this paper studies modeling and identification problems for multi input multirate systems with colored noises the state space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained to solve the difficulty of identification models with unmeasurable noises terms the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates finally the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms

series expansion for a stochastic sandpile using operator algebra we extend the series for the activity density in a one dimensional stochastic sandpile with fixed particle density p the first terms of which were obtained via perturbation theory dickman and vidigal 2002 j phys a math gen 35 7269 the expansion is in powers of the time the coefficients are polynomials in p we devise an algorithm for evaluating expectations of operator products and extend the series to constructing pade approximants to a suitably transformed series we obtain predictions for the activity that compare well against simulations in the supercritical regime

time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

multi attribute target based utilities and extensions of fuzzy measures abstract we introduce a formal description of the target based approach to utility theory for the case of n 1 attributes and point out the connections with aggregation based extensions of capacities our discussion provides economic interpretations of different concepts of the theory of fuzzy measures in particular we analyze the meaning of extensions of capacities based on n dimensional copulas the latter describes stochastic dependence for random vectors of interest in the problem we also trace the connections between the case of 0 1 valued capacities and the analysis of coherent reliability systems

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

adaptive digital control of hammerstein nonlinear systems with limited output sampling this paper is motivated by the practical control considerations that nonlinearity is abundant in industrial processes and output sampling rates are often limited due to hardware constraints in particular for a hammerstein nonlinear sampled data system in which the output sampling period is an integer multiple of the input updating period we derive by using a polynomial transformation technique a mathematical model which is suitable for parameter estimation with dual rate measurement data further we present an adaptive control scheme for such a dual rate nonlinear system the parameter estimation based adaptive algorithm can achieve virtually asymptotically optimal control and ensure that the closed loop system is stable and globally convergent the simulation results are included

scaling behavior of the conserved transfer threshold process we analyze numerically the critical behavior of an absorbing phase transition in the conserved transfer threshold process we determined the steady state scaling behavior of the order parameter as a function of both the control parameter and an external field conjugated to the order parameter the external field is realized as a spontaneous creation of active particles which drives the system away from criticality the obtained results yield that the conserved transfers threshold process belongs to the universality class of absorbing phase transitions in a conserved field

parameter identification of systems with preload nonlinearities based on the finite impulse response model and negative gradient search abstract this paper considers identification problems of a class of nonlinear systems by introducing a switching function and the finite impulse response model we obtain the identification model of a preload nonlinear system and develop a stochastic gradient algorithm to the parameters of the system furthermore a stochastic gradient algorithm with a forgetting factor is given to improve the identification accuracy a simulation results indicate that the forgetting factor can improve the parameter estimation accuracy

the relaxed gradient based iterative algorithm for solving matrix equations aixbi fi abstract in this paper we first present a relaxed gradient based iterative rgi algorithm for solving matrix equations a 1 x b 1 f 1 and a 2 x b 2 f 2 the idea is from niu et al 2011 xie and ma 2016 in which efficient algorithms were developed for solving the sylvester matrix equations then the rgi algorithm is extended to solve the generalized linear matrix equations of the form a i x b i f i i 1 2 n for any initial value it is proved that the iterative solution converges to their true solution under some appropriate assumptions finally a numerical example is given to illustrate that the introduced iterative algorithm is more efficient than gradient based maximal convergence rate iterative gi algorithm of ding et al 2010 in speed elapsed time and iterative steps

transformations between some special matrices special matrices are very useful in signal processing and control systems this paper studies the transformations and relationships between some special matrices the conditions that a matrix is similar to a companion matrix are derived it is proved that a companion matrix is similar to a diagonal matrix or jordan matrix and the transformation matrices between them are given finally we apply the similarity transformation and the companion matrix to system identification

nonequilibrium lattice models series analysis of steady states a perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state the expansion is expressed directly in terms of the kinetic parameter creation rate rather than in powers of the interaction an algorithm for generating series expansions for local properties is described order parameter series 16 terms and precise estimates of critical properties are presented for the one dimensional contact process and several related models

brief paper making parametric hammerstein system identification a linear problem in this paper we study the identification of parametric hammerstein systems with fir linear parts by a proper normalization and a clever characterization it is shown that the average squared error cost function for identification can be expressed in terms of the inner product between the true but unknown parameter vector and its estimate further the cost function is concave in the inner product and linear in the inner product square therefore the identification of parametric hammerstein systems with fir linear parts is a globally convergent problem and has one and only one local and global minimum this implies that the identification of such systems is a linear problem in terms of the inner product square and any local search based identification algorithm converges globally

performance analysis of the am sg parameter estimation for multivariable systems the auxiliary model based stochastic gradient am sg parameter estimation method is an important identification one this paper analyzes the performances of the am sg estimation algorithm for multiple input single output systems i e multivariable systems under the strong persistent excitation condition the analysis and simulation results indicate that the parameter estimation errors converge to zero

the residual based interactive stochastic gradient algorithms for controlled moving average models this paper derives a residual based interactive stochastic gradient isg parameter estimation algorithm for controlled moving average cma models and studied the performance of the residual based isg algorithm under weaker conditions on statistical properties of the noise compared with the residual based extended stochastic gradient algorithm for identifying cma models the proposed isg algorithm can give highly accurate parameter estimates by the simulation example

hierarchical estimation algorithms for multivariable systems using measurement information abstract with the development of industry information technology many modelling methods have been focusing on the estimation problems of multivariable systems especially for the multivariable systems with output error autoregressive noises from input output measurement information since such a system includes both a parameter vector and a parameter matrix the conventional methods cannot be applied to parameter estimation and modelling in order to solve this difficulty a hierarchical least squares based iterative identification algorithm and a hierarchical generalized least squares identification algorithm are proposed the basic idea is to decompose the system into two fictitious subsystems to estimate the parameters of each subsystem and to coordinate the associated items between the two subsystems the simulation results indicate that the proposed algorithm is effective

decoupling the linear and nonlinear parts in hammerstein model identification the main result of this paper is to show that the linear part can be made decoupled from the nonlinear part in hammerstein model identification therefore identification of the linear part for a hammerstein model becomes a linear problem and accordingly enjoys the same convergence and consistency results as if the unknown nonlinearity is absent

brief estimation of an n l n hammerstein wiener model estimation of a single input single output block oriented model is studied the model consists of a linear block embedded between two static nonlinear gains hence it is called n l n hammerstein wiener model first the model structure is motivated and the disturbance model is discussed the paper then concentrates on parameter estimation a relaxation iteration scheme is proposed by making use of a model structure in which the error is bilinear in parameters this leads to a simple algorithm which minimizes the original loss function the convergence and consistency of the algorithm are studied in order to reduce the variance error the obtained linear model is further reduced using frequency weighted model reduction simulation study will be used to illustrate the method

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

iterative solutions to matrix equations of the form aixbi fi this paper is concerned with the numerical solutions to the linear matrix equations a 1xb 1 f 1 and a 2xb 2 f 2 two iterative algorithms are presented to obtain the solutions for any initial value it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values finally simulation examples are given to verify the proposed convergence theorems

observable state space realizations for multivariable systems this paper derives two canonical state space forms i e the observer canonical form and the observability canonical form from multiple input multiple output systems described by difference equations the state space model is expressed by the first order difference equation and is equivalent to the input output representation more specifically by setting the different state variables the difference equations or the input output representations can be transformed into two observable canonical forms and the canonical state space model can be also transformed into the difference equations finally two examples are given

hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems according to the hierarchical identification principle a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems i e multivariable oema like models which is different from multivariable carma like models as there exist unmeasurable noise free outputs and unknown noise terms in the information vector matrix of the corresponding identification model this paper is by means of the auxiliary model identification idea to replace the unmeasurable variables in the information vector matrix with the estimated residuals and the outputs of the auxiliary model a numerical example is provided

steady state of stochastic sandpile models we study the steady state of the abelian sandpile models with stochastic toppling rules the particle addition operators commute with each other but in general these operators need not be diagonalizable we use their abelian algebra to determine their eigenvalues and the jordan block structure these are then used to determine the probability of different configurations in the steady state we illustrate this procedure by explicitly determining the numerically exact steady state for a one dimensional example for systems of size 12 and also study the density profile in the steady state

global convergence conditions in maximum likelihood estimation maximum likelihood estimation has been widely applied in system identification because of consistency its asymptotic efficiency and sufficiency however gradient based optimisation of the likelihood function might end up in local convergence in this article we derive various new non local minimum conditions in both open and closed loop system when the noise distribution is a gaussian process here we consider different model structures in particular ararmax bj and oe models

non additive multi attribute fuzzy target oriented decision analysis as an emerging area considering behavioral aspects of decision making target oriented decision model lies in the philosophical root of bounded rationality as well as represents the s shaped value function this paper deals with multi attribute decision analysis from target oriented viewpoint first the basic random target oriented decision model is extended to involve three types of target preferences benefit target cost target and equal target next since applying fuzzy set theory in decision analysis allows the decision maker to specify imprecise aspiration levels fuzzy target oriented decision analysis is formulated to model three typical types of fuzzy targets fuzzy min fuzzy max and fuzzy equal also different attitudes are used to derive target achievement functions which can be viewed as a support for probability as psychological distance furthermore we have proved that multi attribute target oriented decision analysis has a similar structure with discrete fuzzy measure and choquet integral hence we propose using discrete fuzzy measure and choquet integral to model non additive multi attribute target oriented decision analysis in particular the l measure is applied to reduce the difficulty of collecting information via a designed bisection search algorithm finally a new product development example is used to illustrate the effectiveness and advantages of our model the main advantages of our target oriented decision model are its abilities to model the fuzzy uncertainty of targets as well as capture the non additive behaviors among targets by means of discrete fuzzy measure and choquet integral

hierarchical least squares based iterative estimation algorithm for multivariable box jenkins like systems using the auxiliary model abstract this paper presents a hierarchical least squares iterative algorithm to estimate the parameters of multivariable box jenkins like systems by combining the hierarchical identification principle and the auxiliary model identification idea the key is to decompose a multivariable systems into two subsystems by using the hierarchical identification principle as there exist the unmeasurable noise free outputs and noise terms in the information vector the solution is using the auxiliary model identification idea to replace the unmeasurable variables with the outputs of the auxiliary model and the estimated residuals a numerical example is given to show the performance of the proposed algorithm

maximum likelihood stochastic gradient estimation for hammerstein systems with colored noise based on the key term separation technique this paper considers the identification problems of hammerstein finite impulse response moving average fir ma systems using the maximum likelihood principle and stochastic gradient method based on the key term separation technique in order to improve the convergence rate a maximum likelihood multi innovation stochastic gradient algorithm is presented the simulation results show that the proposed algorithms can effectively estimate the parameters of the hammerstein fir ma systems

solution of a model of self avoiding walks with multiple monomers per site on the husimi lattice we solve a model of self avoiding walks which allows for a site to be visited up to two times by the walk on the husimi lattice this model is inspired in the domb joyce model and was proposed to describe the collapse transition of polymers with one site interactions only we consider the version in which immediate self reversals of the walk are forbidden the phase diagram we obtain for the grand canonical version of the model is similar to the one found in the solution of the bethe lattice with two distinct polymerized phases a tricritical point and a critical endpoint

brief identification of linear systems with hard input nonlinearities of known structure this paper studies identification of systems with input nonlinearities of known structure for input nonlinearities parameterized by one parameter a deterministic approach is proposed based on the idea of separable least squares the identification problem is shown to be equivalent to an one dimensional minimization problem the method is very effective for several common static and nonstatic input nonlinearities for a general input nonlinearity a correlation analysis based identification algorithm is presented which is shown to be convergent

multi innovation stochastic gradient algorithm for multiple input single output systems using the auxiliary model in order to reduce computational burden and improve the convergence rate of identification algorithms an auxiliary model based multi innovation stochastic gradient am misg algorithm is derived for the multiple input single output systems by means of the auxiliary model identification idea and multi innovation identification theory the basic idea is to replace the unknown outputs of the fictitious subsystems in the information vector with the outputs of the auxiliary models and to present an auxiliary model based stochastic gradient algorithm and then to derive the am misg algorithm by expanding the scalar innovation to innovation vector and introducing the innovation length the simulation example shows that the proposed algorithms work quite well

data filtering based recursive least squares algorithm for hammerstein systems using the key term separation principle this paper concerns parameter identification of hammerstein output error moving average systems with a two segment piecewise nonlinearity by combining the key term separation principle and the data filtering technique we transfer the hammerstein model into two regression identification models and present a data filtering based recursive least squares method to estimate the parameters of these two identification models the proposed algorithm achieves a higher computational efficiency than the standard approach by using covariance matrices of smaller dimensions from the two identification models instead of one identification model in the standard approach

critical behavior of a one dimensional fixed energy stochastic sandpile we study a one dimensional fixed energy version that is with no input or loss of particles of manna s stochastic sandpile model the system has a continuous transition to an absorbing state at a critical value of the particle density and exhibits the hallmarks of an absorbing state phase transition including finite size scaling critical exponents are obtained from extensive simulations which treat stationary and transient properties and an associated interface representation these exponents characterize the universality class of an absorbing state phase transition with a static conserved density in one dimension they differ from those expected at a linear interface depinning transition in a medium with point disorder and from those of directed percolation

auxiliary model based least squares identification methods for hammerstein output error systems abstract the difficulty in identification of a hammerstein a linear dynamical block following a memoryless nonlinear block nonlinear output error model is that the information vector in the identification model contains unknown variables the noise free true outputs of the system in this paper an auxiliary model based least squares identification algorithm is developed the basic idea is to replace the unknown variables by the output of an auxiliary model convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition the simulation results show the effectiveness of the proposed algorithms

auxiliary model based rels and mi els algorithm for hammerstein oema systems this paper considers the identification problem for hammerstein output error moving average oema systems an auxiliary model based recursive extended least squares rels algorithm and an auxiliary model based multi innovation extended least squares mi els algorithm are presented using the multi innovation identification theory the basic idea is to express the system output as a linear combination of the parameters by using the key term separation principle and auxiliary model method the proposed algorithms can give highly accurate parameter estimates the simulation results show the effectiveness of the proposed algorithms

two stage least squares based iterative identification algorithm for controlled autoregressive moving average carma systems a two stage least squares based iterative two stage lsi identification algorithm is derived for controlled autoregressive moving average carma systems the basic idea is to decompose a carma system into two subsystems and to identify each subsystem respectively because the dimensions of the involved covariance matrices in each subsystem become small the proposed algorithm has a high computational efficiency the simulation results indicate that the proposed algorithm is effective

convergence of stochastic gradient estimation algorithm for multivariable arx like systems this paper studies the convergence of the stochastic gradient identification algorithm of multi input multi output arx like systems i e multivariable arx like systems by using the stochastic martingale theory this arx like model contains a characteristic polynomial and differs from the conventional multivariable arx system the results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions the simulation results validate the proposed convergence theorem

path integral representation for a stochastic sandpile we introduce an operator description for a stochastic sandpile model with a conserved particle density and develop a path integral representation for its evolution the resulting exact expression for the effective action highlights certain interesting features of the model for example it is nominally massless and the dynamics is via cooperative diffusion using the path integral formalism we construct a diagrammatic perturbation theory yielding a series expansion for the activity density in powers of time

aggregation based extensions of fuzzy measures we present a method extending fuzzy measures on n 1 n represented as boolean utility functions to n ary aggregation functions utility functions by means of a suitable n ary aggregation function and the mobius transform of the considered fuzzy measure the method generalizes the well known lovasz and owen extensions of nondecreasing pseudo boolean functions linked to fuzzy measures all n ary aggregation functions suitable for the proposed construction are completely characterized including among others all n ary copulas associative extended aggregation functions applicable in the case of an arbitrary arity are also completely characterized

system identification based on hammerstein model we are considering non linear system identification based on the hammerstein model i e a non linear static gain in series with linear dynamics the static gain characteristic is any non linear function f an identification scheme is designed to get estimates of both the plant dynamics model and a set of n different points x f x where n is arbitrarily chosen by the user such a scheme involves least squares and prediction error algorithms as well as algebraic transformations such as singular values decomposition svd interestingly the proposed scheme ensures persistent excitation allowing thus exact model identification in the case of no external disturbances

gradient based and least squares based iterative algorithms for matrix equations axb cxtd f abstract this paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation axb cx t d f the basic idea is to decompose the matrix equation system under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving ax b and axb f the analysis shows that when the matrix equation has a unique solution under the sense of least squares the iterative solution converges to the exact solution for any initial values a numerical example verifies the proposed theorems

identification for multirate multi input systems using the multi innovation identification theory this paper considers identification problems of multirate multi input sampled data systems using the continuous time system discretization technique with zero order holds the mapping relationship state space model between available multirate input and output data is set up the multi innovation identification theory is applied to estimate the parameters of the obtained multirate models and to present a multi innovation stochastic gradient algorithm for the multirate systems from the multirate input output data furthermore the convergence properties of the proposed algorithm are analyzed an illustrative example is given

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

identification of block oriented nonlinear systems starting from linear approximations a survey abstract block oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use many different identification approaches were developed over the years to estimate the parameters of a wide range of block oriented nonlinear models one class of these approaches uses linear approximations to initialize the identification algorithm the best linear approximation framework and the approximation framework or equivalent frameworks allow the user to extract important information about the system guide the user in selecting good candidate model structures and orders and prove to be a good starting point for nonlinear system identification algorithms this paper gives an overview of the different block oriented nonlinear models that can be identified using linear approximations and of the identification algorithms that have been developed in the past a non exhaustive overview of the most important other block oriented nonlinear system identification approaches is also provided throughout this paper

aggregation and signature based comparisons of multi state systems via decompositions of fuzzy measures abstract in the reliability literature several results have been presented to compare binary two states systems often such results are obtained from copula based extensions of fuzzy measures where a fuzzy measure describes the structure of a system and a copula describes the stochastic dependence among the lifetimes of its components other similar results have been obtained in terms of the concept of signature here we extend all those results to multi state systems made up from binary components by suitably constructing corresponding mixed binary systems for such a construction we show how any fuzzy measure can be decomposed as a convex combination of 0 1 valued fuzzy measures and how such a decomposition extends to the corresponding aggregation function for a mixed system we can furthermore consider its signature and so we can also define a signature for the multi state system for mixed systems associated to different multi state systems we can thus obtain different comparison results which can be translated into the corresponding comparisons for the parent multi state systems stochastic comparisons are obtained for the discrete random variables which represent the states of two systems at time t as well the arguments in the paper will be illustrated by means of examples and related remarks

scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension we analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field phys rev lett 85 1803 2000 we determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in d 2 3 4 5 dimensions a comparison of our results and those obtained from a mean field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four

compensation of the rls algorithm for output nonlinearities it is shown how the recursive least squares rls algorithm can be modified to compensate for a priori known errors of linearity in the output measurement a novel signal model is used for this purpose only the nonlinear effects are modeled by an output error model and much of the output measurements are used directly in the regression vector the main benefit with this approach is that the advantages of the rls like quick initial convergence for infinite impulse response models can be retained for small linearity errors at the same time the output nonlinearity is allowed to be noninvertible this can be important to treat for example small deadzones and also to avoid the amplification of additive measurement disturbances such amplification can result from inversion of the output nonlinearity simulations illustrate the performance of the algorithm

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

parameter estimation methods for nonlinear systems this paper discusses parameter estimation problems of nonlinear system modeling two model transformation based estimation methods are proposed the basic idea is to transform a complex nonlinear optimization problem into a linear or simple nonlinear optimization problem which is easy to solve then according to the gradient search principle and the newton method a gradient based iterative algorithm and a newton iterative algorithm are derived to determine the parameters of the nonlinear systems finally a numerical example is provided

on the probabilistic meaning of copula based extensions of fuzzy measures applications to target based utilities and multi state reliability systems abstract aggregations functions that are obtainable as copula based extensions of fuzzy measures may emerge in several applied fields we concentrate attention on the probabilistic interpretation of such objects starting from this issue we point out the related meaning in the context of multi attribute target based utilities and multi state reliability systems analogies and relations between the two fields of decisions under uncertainty and systems reliability have been already remarked in the literature here we prove in particular that aggregation functions specifically emerging in the setting of multi attribute target based utilities and in the setting of multi state systems do exactly share the same analytic structure we will show that this identification emerges naturally when the multi state systems are formed with binary components from a technical viewpoint the comparison between two different representations for the considered aggregations and the specific role of the mobius transform have a basic relevance in the proofs of our results and in the development of related discussions

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed

asymptotic behavior of the order parameter in a stochastic sandpile we derive the first four terms in a series for the order paramater the stationary activity density in the supercritical regime of a one dimensional stochastic sandpile in the two dimensional case the first three terms are reported this is done by reorganizing the pertubation theory derived using a path integral formalism dickman and vidigal j phys a 35 7269 2002 to obtain an expansion for stationary properties since the process has a strictly conserved particle density p the fourier mode n 1 k 0 p when n and so is not a random variable isolating this mode we obtain a new effective action leading to an expansion for in the parameter 1 1 4p this requires enumeration and numerical evaluation of more than 200 000 diagrams for which task we develop a computational algorithm predictions derived from this series are in good accord with simulation results we also discuss the nature of correlation functions and one site reduced distributions in the small high density limit

sandpiles with height restrictions we study stochastic sandpile models with a height restriction in one and two dimensions a site can topple if it has a height of two as in manna s model but in contrast to previously studied sandpiles here the height or number of particles per site cannot exceed two this yields a considerable simplification over the unrestricted case in which the number of states per site is unbounded two toppling rules are considered in one the particles are redistributed independently while the other involves some cooperativity we study the fixedenergy system no input or loss of particles using cluster approximations and extensive simulations and find that it exhibits a continuous phase transition to an absorbing state at a critical value z c of the particle density the critical exponents agree with those of the unrestricted manna sandpile