Prediction error identification methods for stationary stochastic processes

The interaction between viscous stress and diffusion is examined through the use of the Chapman and Cowling method, and the results for a general binary mixture of monatomic gases is obtained. It is demonstrated that the kinetic theory calculation provides a first iteration to the form predicted by statistical mechanics; it also produces a modification in the barodiffusion coefficient that is in more general agreement with the results of the 13-moment method than has been shown previously. Finally, the general equations are modified to permit description of a dusty gas or aerosol of fine particles, and the result is found to differ significantly from a calculation based on the methods of stochastic processes.

Maintaining product quality in cement grinding process in the presence of clinker heterogeneity is a challenging task. Model predictive controllers (MPC) are argued to be one possible solution to handle the variability, and the lack of models that relates clinker heterogeneity with product quality makes the MPC design challenging. This investigation addresses the suitability of two data-driven modelling approaches for cement grinding process-prediction error and subspace identification methods. Data collected from cement grinding process is used to build the model of the same. The collected data is used to build different candidate state-space models using the prediction error and subspace identification methods. The candidate models were validated using Akaike's information criterion and mean square error to study the suitability of these modelling techniques. The validation tests are used to identify the most suitable candidate models for the prediction error and subspace methods. The models developed in this investigation are inputs to design predictive controllers for cement industries and assure product quality in the presence of clinker grindability variations.

The study of quantum stochastic processes presents severe difficulties, both on the theory level as well as on technical grounds. The numerically exact solution remains prohibitive even today. In this paper we review and present new results for three different methods used for the modelling of quantum stochastic processes. These include a mixed quantum classical approach, semiclassical initial value representations of the quantum propagator and the reduced density matrix approach as typified by the quantum Wigner-Fokker-Planck equation. A new semiclassical initial value representation that does away with cumbersome prefactors which depend on the monodromy matrix elements but is exact for a harmonic oscillator is presented and its properties analysed. A recently proposed systematic method for improving semiclassical initial value representations is reviewed. The generalization of the Wigner-Fokker-Planck equation to stochastic processes with memory is obtained by using a novel integral equation representation.

Hyperfinite methods for multidimensional stochastic processes

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to the subject of the random search problem. The motivation behind this special issue is to summarize in a single comprehensive publication, the main aspects (past and present), latest developments, different viewpoints and the directions being followed in this multidisciplinary field. We hope that such a special issue could become a particularly valuable reference for the broad scientific community working with the general random search problem.The Editorial Board has invited Marcos G E da Luz, Alexander Y Grosberg, Ernesto P Raposo and Gandhi M Viswanathan to serve as Guest Editors for the special issue.The general question of how to optimize the search for specific target objects in either continuous or discrete environments whenthe information available is limited is of significant importance in a broad range of fields. Representative examples include ecology(animal foraging, dispersion of populations), geology (oil recovery from mature reservoirs), information theory (automated researchers ofregisters in high-capacity database), molecular biology (proteins searching for their sites, e.g., on DNA ), etc.One reason underlying the richness of the random search problem relates to the `ignorance' of the locations of the randomly located `targets'.A statistical approach to the search problem can deal adequately with incomplete information and so stochastic strategies become advantageous.The general problem of how to search efficiently for randomly located target sites can thus be quantitatively described using the conceptsand methods of statistical physics and stochastic processes.ScopeThus far, to the best of our knowledge, no recent textbook or review article in a physics journal has appeared on this topic. This makes aspecial issue with review and research articles attractive to those interested in acquiring a general introduction to the field. Thesubject can be approached from the perspective of different fields: ecology, networks, transport problems, molecular biology, etc. Thestudy of the problem is particularly suited to the concepts and methods of statistical physics and stochastic processes; for example, fractals,random walks, anomalous diffusion. Discrete landscapes can be approached via graph theory, random lattices and complex networks. Such topics areregularly discussed in Journal of Physics A: Mathematical and Theoretical. All such aspects of the problem fall within the scope and focus of thisspecial issue on the random search problem: trends and perspectives.Editorial policyAll contributions to the special issue will be refereed in accordance with the refereeing policy of the journal. In particular, all researchpapers will be expected to be original work reporting substantial new results. The issue will also contain a number of review articles byinvitation only. The Guest Editors reserve the right to judge whether a contribution fits the scope of the special issue.Guidelines for preparation of contributions We aim to publish the special issue in August 2009. To realize this, the DEADLINE for contributed papers is 15 January 2009. There is a page limit of 15 printed pages (approximately 9000 words) per contribution. For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on document preparation can be found at www.iop.org/Journals/jphysa. Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'J. Phys. A Special Issue— Random Search Problem'. Please state whether the paper has been invited or is contributed. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing electronic code on CD if available and quoting 'J. Phys. A Special Issue—Random Search Problem'. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. This special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue.

Empirical bayes regionalization methods for spatial stochastic processes : Butcher, J B; Medina, M A; Marin, C M Water Resour ResV27, N1, Jan 1991, P7–15

We present in a rather pedagogical way a new formulation of quantum mechanics. Our starting point is the path integral representation of the quantum-mechanical propagator analytically continued to imaginary timeW(X″, s″|X′, s′). We view the set of random paths contributing toW(X″, s″|X′, s′) as the manifold of solutions of a Langevin equation with a Gaussian white noise. We thus obtainW(X″, s″|X′, s′) as the noise-average of a suitable functional of the solution of the Langevin equation. The standard quantum-mechanical propagator is finally recovered by analytically continuingW(X″, s″|X′, s′) back to real time. The present approach allows for a straightforward application of standard methods of classical stochastic processes to quantum-mechanical problems and offers a new promising way to perform computer simulations of quantum-dynamical systems.

In this thesis we introduce Non-Standard Methods, in particular the use of hyperfinite difference equations, to the study of space-time random processes. We obtain a new existence theorem in the spirit of Keisler (1984) for the one dimensional heat equation forced non-linearly by white noise. We obtain several new results on the sample path properties of the Critical Branching Measure Diffusion, and show that in one dimension it has a density which satisfies a non-linearly forced heat equation. We also obtain results on the dimension of the support of the Fleming-Viot Process.

Purpose:The detection of abdomino-pelvic tumors embedded in or nearby radioactive urine containing 18F-FDG activity is a challenging task on PET/CT scan. In this study, we propose and validate the suprathreshold stochastic resonance-based image processing method for the detection of these tumors.Methods:The method consists of the addition of noise to the input image, and then thresholding it that creates one frame of intermediate image. One hundred such frames were generated and averaged to get the final image. The method was implemented using MATLAB R2013b on a personal computer. Noisy image was generated using random Poisson variates corresponding to each pixel of the input image. In order to verify the method, 30 sets of pre-diuretic and its corresponding post-diuretic PET/CT scan images (25 tumor images and 5 control images with no tumor) were included. For each sets of pre-diuretic image (input image), 26 images (at threshold values equal to mean counts multiplied by a constant factor ranging from 1.0 to 2.6 with increment step of 0.1) were created and visually inspected, and the image that most closely matched with the gold standard (corresponding post-diuretic image) was selected as the final output image. These images were further evaluated by two nuclear medicine physicians.Results:In 22 out of 25 images, tumor was successfully detected. In five control images, no false positives were reported. Thus, the empirical probability of detection of abdomino-pelvic tumors evaluates to 0.88.Conclusion:The proposed method was able to detect abdomino-pelvic tumors on pre-diuretic PET/CT scan with a high probability of success and no false positives.

Performance of planned activities not always leads to the achievement of planned results in innovation projects with a high degree of uncertainty. Management of such specific projects requires the usage of specific methods and processes. It is necessary to develop own stochastic process methods rather than use classical methods of deterministic management. The main peculiarity of stochastic processes of projects consists in the inability to carry out more than one experiment. Implementation of a project is a stochastic process, which is carried out only once. For the purposes of the research, stochastic project management is the process of organisation, planning and control over projects, in which the decisions and actions of managers are described by stochastic functions. If the project realisation is described by stochastic processes, the project management process is indeed described by stochastic processes. This research suggests a project management approach based on the focus on the project product and project management as stochastic processes based on stochastic functions. It is demonstrated that stochastic function values, which underlie the stochastic processes, are formed by the intellectual instruments of those involved in the project and are developed on the basis of their knowledge and skills. The latter, in turn, are the result of studying and practical work on the project. Therefore, it is difficult to predict decisions and actions of managers and contractors, even if internal and external influences on them are specified. Then, any decisions or actions of such persons with regard to the external observer are described by stochastic functions. The purpose of this study is to describe the processes of stochastic project management. The purpose of the study is the project management process. The subject of research is the methods of stochastic project management. Within the framework of the study, all groups of processes of stochastic control will be mathematically described and the conditions of their impact determined. The processes of stochastic project management are outlined and formally presented. These are the processes of project management organisation, the processes of project management support, processes of project content definition, processes of defining the resources, required for the project works, processes of project planning, processes of influence on contractors of actions (works).

Power optimization based on intelligent algorithm draws more and more attention. This article presents a novel low power optimization strategy based on the high level software power management employing Markov Process for charactering the real running workload. This article formulates workload characterization and selection with stochastic process method, and solves the formula using dynamic voltage frequency scaling base on microprocessor. Based on Markov process, the multi-parameter constraints has been employed to exploit the optimization space. Comparing with existing power optimization algorithm, our proposed power optimization algorithm doesn't need any prior data and maintains a value function representing expected reward. As many hardware events can be effectively captured and modeled, this optimization technique is capable to explore an ideal tradeoff in the constraint space.

A Monte Carlo algorithm is developed for generating samples of arbitrary real-valued nonstationary Gaussian processes. The algorithm is based on representations of these processes by finite sums of harmonics with dependent Gaussian coefficients, in contract to similar representations available for stationary Gaussian processes that have independent Gaussian coefficients. The proposed algorithm is based on an idea in [Grigoriu, J. Eng. Mech., ASCE 119: 328–343, 1993]. It is shown that the covariance matrix of the random coefficients in the representation proposed for nonstationary Gaussian processes can be obtained simply from ordinates of the generalized spectral densities of these processes. Two numerical examples are presented to illustrate the application of the proposed algorithm and assess its performance. The examples are a stationary Gaussian process and a nonstationary Gaussian process obtained from a stationary process by distorting its time scale.

Introduction.The purpose of this paper is to study the Fourier transforms of the sample functions x(i) of random processes for which a moment E | x(i) |p is finite and bounded in t for some p > 0; for example, stationary processes with E | x(0) |p finite.x(t) will not in general approach 0 at oo and its Fourier transform will not usually be a function, but can be defined as a tempered distribution in Schwartz's theory [8].The main result is that if p > 1 the Fourier transform of x(i) is a "Stieltjes integral," i.e. it is obtained from a locally integrable function by differentiating once in the sense of distributions.Since local properties of the Fourier transform have little to do with local properties of x(i), it is not surprising that the same thing is true if x(f) is replaced by a "random distribution," i.e. a process possibly so irregular that values x(i0) at points i0 are not defined, but with averages " J"x(t)/(t)di" for smooth functions / defined ; we require pth moments of such averages bounded under translation of /.It is also possible to replace the real line as domain of values for t by a Euclidean space of arbitrary dimension k ; here a Stieltjes integral is of the form dkF¡Bty ••• dtk with F locally integrable, and this is the form of the Fourier transforms, again for p > 1.The results are stated in detail in §2.The positive assertions for p > 1 are proved in § §4-6, and the counter-examples for p :g 1 are given in §7.§ §1 and 3 deal with random distributions in general.§8 shows that the results are easily adapted to the case of processes with nonnegative or discrete parameter or stationary increments.For stationary Gaussian processes, the results appeared in my Princeton thesis, written with the helpful advice of G. A. Hunt and Edward Nelson.There the methods were based on Ito's "spectral measure," requiring both second moments and strict stationarity of the process or its increments ([4], [5]); here using other methods, essentially the Hausdorff-Young inequality, almost as much is proved from much more general hypotheses.1. Random distributions.A random distribution, as defined by Gel'fand [1], is a mapping f-*L(J) of a space S> = £$(Rk), i.e. the space of C°° functions with

Previous article Next article Second-Order Markov and Reciprocal Stationary Gaussian ProcessesR. N. MiroshinR. N. Miroshinhttps://doi.org/10.1137/1124099PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. N. Bernshtei˘n, On the dependencies among random variablesCollected Works, Vol. IV, Nauka, Moscow, 1964, 235–254, (In Russian.) Google Scholar[2] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[3] Benton Jamison, Reciprocal processes: The stationary Gaussian case, Ann. Math. Statist., 41 (1970), 1624–1630 MR0267637 0248.60030 CrossrefGoogle Scholar[4] I. I. Gikhman and , A. V. Skorokhod, The Theory of Stochastic Processes, Vol. I, Springer-Verlag, New York, 1974 CrossrefGoogle Scholar[5] E. Kamke, Differentialgleichungen. Lösungsmethoden and Lösungen, Vol. 1, Chelsea, New York, 1974 Google Scholar[6] E. Wong, Some results concerning the zero-crossings of Gaussian noise, SIAM J. Appl. Math., 14 (1966), 1246–1254 10.1137/0114099 MR0207059 0147.15905 LinkGoogle Scholar[7] E. Wong, The distribution of intervals between zeros for a stationary Gaussian process, SIAM J. Appl. Math., 18 (1970), 67–73 10.1137/0118008 MR0256456 0221.60024 LinkGoogle Scholar[8] R. N. Miroshin, Convergence of Rice and Longuet-Higgins series for a Wong process, Theory Prob. Applications, 21 (1976), 863–866 10.1137/1121103 0374.60049 LinkGoogle Scholar[9] R. N. Miroshin, Asymptotics of the second factorial moment of the number of upward crossings of the line $kt+a$ by a Gaussian stationary process, Vestnik Leningrad. Univ., 23 (1968), 109–120 MR0235612 0165.52602 Google Scholar[10] M. Krein, Sur le problème du prolongement des fonctions hermitiennes positives et continues, C. R. (Doklady) Acad. Sci. URSS (N.S.), 26 (1940), 17–22 MR0004333 0022.35302 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Characterization of Multivariate Stationary Gaussian Reciprocal DiffusionsJournal of Multivariate Analysis, Vol. 62, No. 1 Cross Ref Gaussian reciprocal diffusions and positive definite sturm-liouville operators4 April 2007 | Stochastics and Stochastic Reports, Vol. 55, No. 3-4 Cross Ref Gaussian reciprocal processes revisitedStatistics & Probability Letters, Vol. 12, No. 4 Cross Ref Reciprocal covariance solutions of some matrix differential equationsStochastic Processes and their Applications, Vol. 37, No. 1 Cross Ref Characterization and Classification of Gaussian Second Order Reciprocal Processes Cross Ref Gaussian reciprocal processes and self-adjoint stochastic differential equations of second order2 May 2007 | Stochastics and Stochastic Reports, Vol. 34, No. 1-2 Cross Ref Reciprocal diffusions and stochastic differential equations of second order ∗Stochastics, Vol. 24, No. 4 Cross Ref Multivariate reciprocal stationary Gaussian processesJournal of Multivariate Analysis, Vol. 23, No. 1 Cross Ref On Miroshin’s Second-Order Reciprocal ProcessesJulia Abrahams3 August 2006 | SIAM Journal on Applied Mathematics, Vol. 44, No. 1AbstractPDF (316 KB)The Use of Rice SeriesR. N. Miroshin28 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 4AbstractPDF (1011 KB)The zero-crossing problem for some nonstationary Gaussian processes (Corresp.)IEEE Transactions on Information Theory, Vol. 28, No. 4 Cross Ref Convergence of Longuet-Higgins Series for Stationary Gaussian Markov Processes of First OrderR. N. Miroshin17 July 2006 | Theory of Probability & Its Applications, Vol. 26, No. 1AbstractPDF (1546 KB) Volume 24, Issue 4| 1980Theory of Probability & Its Applications History Submitted:11 July 1977Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1124099Article page range:pp. 845-852ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

This article is devoted to methods of processing random processes. This task becomes particularly relevant in cases where the random process is broadband and non-stationary; then, the measurement of a random process can be associated with an assessment of its probabilistic characteristics. Very often, a non-stationary broadband random process is represented by a single implementation with a priori uncertainty about the type of distribution function. Such random processes occur in information and measuring communication systems in which information is transmitted at a real-time pace (for example, radio telemetry systems in spacecraft). The use of methods of traditional mathematical statistics, for example, maximum likelihood methods, to determine probability characteristics in this case is not possible. In addition, the on-board computing systems of spacecraft operate under conditions of restrictions on mass-dimensional characteristics and energy consumption. Therefore, there is a need to apply accelerated methods of processing measured random processes. This article discusses a method of processing non-stationary broadband random processes based on the use of non-parametric methods of decision theory. An algorithm for dividing the observation interval into stationary intervals using non-parametric Kendall’s statistics is considered, as are methods for estimating probabilistic characteristics on the stationary interval using ordinal statistics. This article presents the results of statistical modeling using the Mathcad program.