recursive estimation methods for discrete systems in system identification the error evolution is composed of two decoupled parts one is the identifying information on the current estimation residual while the other is past arithmetic errors previous recursive algorithms only considered how to update current prediction errors up to now research has mostly been based on recursive least squares rls methods in this note a general recursive identification method is proposed for discrete systems using this new algorithm a recursive empirical frequency domain optimal parameter refop estimate is established the refop method has the advantage of resisting disturbance noise some simulations are included to illustrate the new method s reliability

simulation of stopped diffusions in this work we study standard euler updates for simulating stopped diffusions as an immediate application we discuss the computation of first exit times of diffusions from a domain we focus on one dimensional situations and show how the ideas for the simulation of killed diffusions can be adapted to this problem in particular we give a fully implementable algorithm to compute the first exit time from an interval numerically the brownian motion case is treated in detail and extensions to general diffusions are given special emphasis is given to numerical experiments for every ansatz we include numerical experiments confirming the conjectured accuracy of our methods our algorithm is of order one in a weak sense comparisons with other algorithms are shown results that are superior to those obtained with other methods are presented when approximating a first hitting time distribution the results obtained with our algorithm are much better than those achieved with other methods

brownian excursions on combs in this paper we use techniques from ito excursion theory to analyze brownian motion on generalized combs ito excursion theory is a little known area of probability theory and we therefore present a brief introduction for the uninitiated a general method for analyzing transport along the backbone of the comb is demonstrated and the specific case of a comb whose teeth are scaling branching trees is examined we then present a recursive method for evaluating the distribution of the first passage times on hierarchical combs

model identification of a noncausal 2 d ar process using a causal 2 d ar model on the nonsymmetric half plane if a noncausal two dimensional 2 d autoregressive ar process is bi causal there exists a causal 2 d ar process on the nonsymmetric half plane having the same autocorrelations as the noncausal 2 d ar process a formula is presented to relate the ar coefficients of the noncausal 2 d ar process with those of the causal 2 d ar process on the nonsymmetric half plane the 2 d yule walker equations are derived for causal 2 d ar models on the nonsymmetric half plane a computationally efficient order recursive algorithm is proposed to solve the 2 d yule walker equations using the autocorrelation equivalence relation and the order recursive algorithm we can easily identify a noncausal 2 d ar process from its autocorrelations

a rank test based approach to order estimation i 2 d ar models application in system identification and parametric spectral estimation by two dimensional 2 d autoregressive ar and 2 d autoregressive moving average arma models the order selection problem is often required in this correspondence we show that the information of 2 d ar model order is implicitly contained in a correlation matrix an algorithm for 2 d quarter plane ar model order determination is proposed numerical simulations are presented to show the efficiency of the proposed singular value decomposition svd based algorithm

critical frequencies and parameters for linear delay systems a lyapunov matrix approach abstract a new method based on recent results concerning the construction of the lyapunov matrix of delay systems reveals conditions under which the characteristic function has a root s 0 such that s 0 is also a root as the pure imaginary roots which are crucial in the stability analysis of time delay systems are of that type this method gives rise to a novel approach for the delay independent and delay dependent stability analyses of systems with delay that are multiple of a basic delay distributed delays and of a class of neutral type time delay systems a number of examples are given to illustrate the approach and to show its strength

quiet direct simulation monte carlo with random timesteps use of a high order deterministic sampling technique in direct simulation monte carlo dsmc simulations eliminates statistical noise and improves computational performance by orders of magnitude in this paper it is also shown that if a random timestep is used in place of a fixed timestep there is an additional improvement in performance this performance can be increased by using a timestep that samples a random variable with a high kurtosis probability density function as a simple example of the method the one dimensional diffusion equation with an exponentially distributed timestep is simulated and a performance gain of approximately two is obtained applications to numerical simulations of fluids and plasmas are indicated

handbook of brownian motion facts and formulae i theory i stochastic processes in general ii linear diffusions iii stochastic calculus iv brownian motion v local time as a markov process vi differential systems associated to brownian motion appendix 1 briefly on some diffusions ii tables of distributions of functionals of brownian motion and related processes 1 brownian motion 2 brownian motion with drift 3 reflecting brownian motion 4 bessel process of order 5 bessel process of order 1 2 6 bessel process of order zero 7 ornstein uhlenbeck process 8 radial ornstein uhlenbeck process 9 geometric brownian motion appendix 2 special functions appendix 3 inverse laplace transforms appendix 4 differential equations and their solutions appendix 5 formulae for n fold differentiation

a maximum likelihood approach to texture classification a new approach to texture classification is described which is based on measurements of the spatial gray level co occurrence probability matrix this approach can make use of assumed stochastic models for texture in imagery and is an approximation to the statistically optimum maximum likelihood classifier the efficacy of the approach is demonstrated through experimental results obtained with real world texture data

asymptotic generalized eigenvalue distribution of block multilevel toeplitz matrices in many detection and estimation problems associated with processing of second order stationary random processes the observation data are the sum of two zero mean second order stationary processes the process of interest and the noise process in particular the main performance criterion is the signal to noise ratio snr after linear filtering the optimal snr corresponds to the maximal value of a rayleigh quotient which can be interpreted as the largest generalized eigenvalue of the covariance matrices associated with the signal and noise processes which are block multilevel toeplitz structured for m dimensional vector valued second order stationary p dimensional random processes xi1 i2 ip isin bbr m in this paper an extension of szego s theorem to the generalized eigenvalues of hermitian block multilevel toeplitz matrices is given providing information about the asymptotic distribution of those generalized eigenvalues and in particular of the optimal snr after linear filtering a simple proof of this theorem under the hypothesis of absolutely summable elements is given the proof is based on the notion of multilevel asymptotic equivalence between block multilevel matrix sequences derived from the celebrated gray approach finally a short example in wideband space time beamforming is given to illustrate this theorem

fast simulations of stochastic dynamical systems a number of features relevant to stochastic dynamical systems such as moments of solutions and first passage times can be efficiently computed resorting to sequences of quasi random numbers low discrepancy sequences this method represents an alternative choice to the use of pseudorandom numbers provided that a special care is paid to keep sufficiently uncorrelated as well as uniform the former sequences

characterization and estimation of two dimensional arma models a class of finite order two dimensional autoregressive moving average arma is introduced that can represent any process with rational spectral density in this model the driving noise is correlated and need not be gaussian currently known classes of arma models or ar models are shown to be subsets of the above class the three definitions of markov property are discussed and the class of arma models are precisely stated which have the noncausal and semicausal markov property without imposing any specific boundary conditions next two approaches are considered to estimate the parameters of a model to fit a given image the first method uses only the empirical correlations and involves the solution of linear equations the second method is the likelihood approach since the exact likelihood function is difficult to compute we resort to approximations suggested by the toroidal models numerical experiments compare the quality of the two estimation schemes finally the problem of synthesizing a texture obeying an arma model is considered

probabilistically induced domain decomposition methods for elliptic boundary value problems monte carlo as well as quasi monte carlo methods are used to generate only few interfacial values in two dimensional domains where boundary value elliptic problems are formulated this allows for a domain decomposition of the domain a continuous approximation of the solution is obtained interpolating on such interfaces and then used as boundary data to split the original problem into fully decoupled subproblems the numerical treatment can then be continued implementing any deterministic algorithm on each subdomain both monte carlo or quasi monte carlo simulations and the domain decomposition strategy allow for exploiting parallel architectures scalability and natural fault tolerance are peculiarities of the present algorithm examples concern helmholtz and poisson equations whose probabilistic treatment presents additional complications with respect to the case of homogeneous elliptic problems without any potential term and source

domain decomposition solution of elliptic boundary value problems via monte carlo and quasi monte carlo methods domain decomposition of two dimensional domains on which boundary value elliptic problems are formulated is accomplished by probabilistic monte carlo as well as by quasi monte carlo methods generating only a few interfacial values and interpolating on them continuous approximations for the trace of solution are thus obtained to be used as boundary data for the subproblems the numerical treatment can then proceed by standard deterministic algorithms separately in each of the so obtained subdomains monte carlo and quasi monte carlo simulations may naturally exploit multiprocessor architectures leading to parallel computing as well as the ensuing domain decomposition does the advantages such as scalability obtained by increasing the number of processors are shown both theoretically and experimentally in a number of test examples and the possibility of using clusters of computers grid computing is emphasized

lyapunov matrices for neutral time delay systems with exponential kernel abstract in this contribution we study the problem of finding a lyapunov matrix for neutral type systems with distributed delay and exponential kernel in previous works an attempt was made to reduce this problem to the computation of solutions to an auxiliary delay free system with boundary conditions in this paper we propose new boundary conditions allowing a significant extension of existing results it is established that the new auxiliary boundary value problem has a unique solution if and only if there exists a unique lyapunov matrix

domain decomposition solution of nonlinear two dimensional parabolic problems by random trees a domain decomposition method is developed for the numerical solution of nonlinear parabolic partial differential equations in any space dimension based on the probabilistic representation of solutions as an average of suitable multiplicative functionals such a direct probabilistic representation requires generating a number of random trees whose role is that of the realizations of stochastic processes used in the linear problems first only few values of the sought solution inside the space time domain are computed by a monte carlo method on the trees an interpolation is then carried out in order to approximate interfacial values of the solution inside the domain thus a fully decoupled set of sub problems is obtained the algorithm is suited to massively parallel implementation enjoying arbitrary scalability and fault tolerance properties pruning the trees is shown to increase appreciably the efficiency of the algorithm numerical examples conducted in 2d including some for the kpp equation are given

a new approach for subset 2 d ar model identification for describing textures this paper addresses the problem of identification of appropriate autoregressive ar components to describe textural regions of digital images by a general class of two dimensional 2 d ar models in analogy with univariate time series the proposed technique first selects a neighborhood set of 2 d lag variables corresponding to the significant multiple partial auto correlation coefficients a matrix is then suitably formed from these 2 d lag variables using singular value decomposition svd and orthonormal with column pivoting factorization qrcp techniques the prime information of this matrix corresponding to different pseudoranks is obtained schwarz s 1978 information criterion sig is then used to obtain the optimum set of 2 d lag variables which are the appropriate autoregressive components of the model for a given textural image a four class texture classification scheme is illustrated with such models and a comparison of the technique with the work of chellappa and chatterjee 1985 is provided

multidimensional multiple order complex parametric model identification this paper presents a way to access both the multiple order and parameters of a multidimensional complex number autoregressive ar model through matrix factorization the principle of this technique consists of the transformation of the multidimensional model to a pseudo simple input simple output ar model then performing factorization of the covariance matrix of the data this factorization then leads to a recursive form of the parameter and order estimation this paper makes two principal contributions the first is a generalization of one dimensional factored form algorithm and the second is that it makes it possible to access all the possible different orders and parameters of a multidimensional complex number ar model of any dimension whereas classical approaches are limited to at most four dimensional models computer simulation results are provided to illustrate the behavior of this method

efficient numerical solution of stochastic differential equations using exponential timestepping we present an exact timestepping method for brownian motion that does not require gaussian random variables to be generated time is incremented in steps that are exponentially distributed random variables boundaries can be explicitly accounted for at each timestep the method is illustrated by numerical solution of a system of diffusing particles

3 d ar model order selection via rank test procedure this paper deals with the problem of three dimensional autoregressive 3 d ar model order estimation we show that the information for the 3 d ar model order is implicitly contained in an appropriate matrix rank built from the autocorrelation function acf of the underlying 3 d gaussian process exploiting this property we develop an algorithm to estimate the order p1 p2 p3 corresponding to the quarter space qs region of support the proposed method is based upon a rank test procedure rtp using singular value decomposition svd and solving nonlinear system equations numerical simulations are presented to illustrate the performances of the proposed algorithm

stochastic calculus application to dynamic bifurcations and threshold crossings for the dynamic pitchfork bifurcation in the presence of white noise the statistics of the last time at zero are calculated as a function of the noise level and the rate of change of the parameter the threshold crossing problem used for example to model the firing of a single cortical neuron is considered concentrating on quantities that may be experimentally measurable but have so far received little attention expressions for the statistics of pre threshold excursions occupation density and last crossing time of zero are compared with results from numerical generation of paths

two chi square statistics for determining the orders p and q of an arma p q process the theta lambda and eta functions have been previously proposed for use in choosing the autoregressive and moving average orders of an arma q p process visually two chi square statistics associated with these three functions are presented and used here to determine the orders of an arma process statistically it is shown that the two statistics are asymptotically equivalent to the quenouille walker s goodness of fit test statistic which is a lagrange multiplier test statistic some numerical examples are presented to illustrate the usefulness of the two chi square statistics as well as the three functions in arma modeling

lyapunov matrices for a class of neutral type time delay systems a class of neutral type time delay systems is presented for which computation of lyapunov matrices is reduced to a solution of an auxiliary delay free system of linear differential matrix equations with a special set of two point boundary conditions

an exponential timestepping algorithm for diffusion with discontinuous coefficients abstract we present a new monte carlo algorithm to simulate diffusion processes in presence of discontinuous convective and diffusive terms the algorithm is based on the knowledge of close form analytic expressions of the resolvents of the diffusion processes which are usually easier to obtain than close form analytic expressions of the density in the case of diffusion processes with piecewise constant coefficients known as skew diffusions such close form expressions for the resolvent are available then we apply our algorithm to this particular case and we show that the approximate densities of the particles given by the algorithm replicate the particularities of the true densities well discontinuities bimodality besides numerical experiments show a quick convergence

multidimensional exponential timestepping with boundary test exponential timestepping algorithms are efficient for exit time problems because a boundary test can be performed at the end of each timestep giving high order convergence in numerical evaluation of mean exit times successive time increments are independent random variables with an exponential distribution we show how to perform exact timestepping for brownian motion in more than one dimension and consider hitting times of curved surfaces taking as examples the exit times from a circle from a ball from an ellipse and from the region bounded by the two lines of a hyperbola we report the results of numerical experiments performed with the algorithms developed in this work

exponential timestepping with boundary test for stochastic differential equations we present new numerical methods for scalar stochastic differential equations successive time increments are independent random variables with an exponential distribution we perform numerical experiments using a double well potential exponential timestepping algorithms are efficient for escape time problems because a simple boundary test can be performed at the end of each step

modeling 2 d ar processes with various regions of support we show that there exists a causal 2 d linear process in the nonsymmetric half plane having the same autocorrelations as a noncausal 2 d linear process in the whole plane this property is called the autocorrelation equivalence relation and can be used for practical fitting and modeling of 2 d processes some causal 2 d autoregressive ar models with various regions of support are considered such as half cross half diamond quarter plane square half square half hexagon half octagon and half circle considerations of parsimony in 2 d model fitting are then focused not only on the number of parameters in our model but also most importantly on the optimal shape of the region of support their 2 d yule walker equations are derived and a computationally efficient order recursive algorithm is proposed to solve them the autocorrelation equivalence relation and the order recursive algorithm are utilized to specify a noncausal 2 d ar process as well as its spectrum from a given realization of a random field

robust variance reduction for random walk methods random walk methods are effective for solving linear partial differential equations in many dimensions especially those involving complex geometries they are based on an equivalence given by a feynman kac formula between an expectation of a functional of a stochastic process and the solution at a point of a partial differential equation the drawback is that the error is proportional only to the square root of the reciprocal of the number of trials efficiency depends critically on variance reduction a general strategy for doing this in the case of stochastic differential equations is proposed by milstein the idea is to introduce a bias in the drift term and to exactly compensate for this by unequal weighting of the trials there is an optimal bias defined in terms of the solution of the partial differential equation which reduces the variance to zero in practice an approximation is used this idea has been tested under the name biased brownian dynamics on the problem of calculating rate constants for diffusion limited reactions the approach is successful in some cases but is less successful in more difficult cases due to the occasional occurrence of a well above average weight proposed and tested here is a weight control algorithm which greatly enhances the effectiveness of biased brownian dynamics

optimum quarter plane autoregressive modeling of 2 d fields using four field lattice approach a new orthogonal four field two dimensional 2 d quarter plane lattice structure with a complete set of reflection coefficients is developed by employing appropriately defined auxiliary prediction errors this work is the generalization of the three parameter lattice filter proposed by parker and kayran 1984 after the first stage four auxiliary forward and four auxiliary backward prediction errors are generated in order to obtain a growing number of 2 d reflection coefficients at successive stages the theory has been proven by using a geometrical formulation based on the mathematical concepts of vector space orthogonal projection and subspace decomposition it is shown that all four quarter plane filters are orthogonal and thus optimum for all stages in addition to developing the basic theory a set of orthogonal backward prediction error fields for successive lattice parameter model stages is presented

an order recursive algorithm to solve the 3 d yule walker equations of causal 3 d ar models an order recursive algorithm is proposed to solve the 3 d yule walker equations of causal 3 d ar models it is computationally efficient and can be easily transformed into a computer program moreover it can be utilized to determine the orders of a causal 3 d ar process

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

distribution of domain sizes in the zero temperature glauber dynamics of the one dimensional potts model for the zero temperature glauber dynamics of the q state potts model we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one species coagulation model a1a a in the long time limit this distribution is universal and from its complicated exact expression we extract its behavior in various regimes our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently considering the dynamics of domain walls as a reaction diffusion model a1a a with probability q22 q21 and a1a f with probability 1 q21 we calculate the pair correlation function in the long time regime s1063 651x 96 12809 9

brief paper lyapunov matrices existence and uniqueness issues a necessary and sufficient condition for the existence and uniqueness of lyapunov matrices for neutral type single delay systems is presented

three dimensional textured image blocks model based on wold decomposition in this paper we present a new parametric modeling of three dimensional homogeneous volumes of textured images 3d texture based on 3d wold decomposition for discrete processes this decomposition additively separates any 3d discrete homogeneous process into three mutually orthogonal components a purely indeterministic a remote past type deterministic and an evanescent component the evanescent component can be further decomposed into two orthogonal components called type 1 evanescent and type 2 evanescent assuming that the 3d image volume is a finite realization of a discrete homogeneous stochastic process the 3d texture field can be uniquely represented as a sum of four mutually orthogonal components with different spectral properties the aim of this paper is to present new parametric models able to describe both the spectral support and spatial characteristics of each component a spectral decomposition algorithm to separate a 3d texture into structured and unstructured parts is also proposed