Showing papers on "Continuous-time stochastic process published in 1987"
Book•
01 Oct 1987
TL;DR: Stochastic Processes Linear Stochastic Systems Estimation Theory Stochastics Realization Theory System Identification: Foundations and Basic Concepts.
Abstract: Stochastic Processes Linear Stochastic Systems Estimation Theory Stochastic Realization Theory System Identification: Foundations and Basic Concepts Least Squares Parameter Estimation Maximum Likelihood Estimation of Gaussian Armax and State-Space System Minimum Prediction Error Identification Methods Non-Stationary System Identification Feedback, Causality, and Closed Loop System Identification Linear-Quadratic Stochastic Control Stochastic Adaptive Control Appendix 1: Probability Theory Appendix 2: System Theory Appendix 3: Harmonic Analysis.
728 citations
TL;DR: In this paper, the authors present an Introduction to Random Processes, With Applications to Signals and Systems, with a focus on the application of random processes to signal and signal processing.
Abstract: (1987). Introduction to Random Processes, With Applications to Signals and Systems. Technometrics: Vol. 29, No. 2, pp. 245-246.
317 citations
TL;DR: It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model.
Abstract: Stochastic techniques have assumed a prominent role in computer graphics because of their success in modeling a variety of complex and natural phenomena. This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct high-quality random functions, including those with non-fractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique.
159 citations
Book•
11 Feb 1987
TL;DR: A chaffer sieve support for a combine harvester which facilitates sieve installation and removal and also confines the grain to the cleaning area of the sieve so that there will be no passage of grain laterally over the side frame members thereof.
Abstract: A chaffer sieve support for a combine harvester which facilitates sieve installation and removal and also confines the grain to the cleaning area of the sieve so that there will be no passage of grain laterally over the side frame members thereof. A pair of support angles embrace the side frame members of the chaffer sieve and are pivoted at their forward ends to the side rails of the grain pan for limited swinging movement between a raised clamped position wherein, in combination with a pair of lateral flanges on the grain pan side rails, they define sieve-receiving channels, and a lowered inclined position wherein they release the sieve and, in effect, provide a ramp on which the sieve may be slid rearwardly and downwardly for removal purposes. In the raised position of the support angles, the side frame members of the chaffer sieve are entirely confined within the chanels and thus only the effective cleaning area of the sieve is exposed to the grain for cleaning purposes.
115 citations
TL;DR: A process of O-U type is a mild solution of the stochastic differential system in Hilbert space dXt=AX t dt+dZ t, where A generates a semigroup of operators and Z tis a process with homogeneous independent increments as mentioned in this paper.
Abstract: A process fo Ornstein-Uhlenbeck type is a mild solution of the stochastic differential system in Hilbert space dXt=AX t dt+dZ t, where A generates a semigroup of operators and Z tis a process with homogeneous independent increments. The explicit integral formula for the process of O-U type is given. The main purpose is to study stationary distributions for such processes. Sufficient and necessary conditions for existence and characterization are given. The difference between finite and infinite dimensional cases is illustrated by examples
73 citations
TL;DR: In this paper, the authors apply Markov Process Theory to nonlinear random vibration problems and estimate approximate methods in non-Linear Stochastic Dynamics for structural damage analysis of reinforced concrete buildings.
Abstract: 1 Basic Principles of Probability, Stochastic Processes and Reliability Methods.- 2 Stochastic Dynamic Analysis of Linear Systems.- 3 Stochastic Fields and Their Digital Simulation.- 4 Application of Markov Process Theory to Nonlinear Random Vibration Problems.- 5 Approximate Methods in Non-Linear Stochastic Dynamics.- 6 Seismic Damage Analysis of Reinforced Concrete Buildings.- Appendices.- A Linearization Coefficients.- B Details of Damaged Buildings.- Author Index.
57 citations
TL;DR: In this article, the authors define a stochastic process called the due date process which models the times at which these tasks are completed, and derive conditions under which this process is stable.
Abstract: Human endeavors are often planned to be completed at some predefined times. In reality, these tasks are completed either before or after the planned times. In this paper, we define a stochastic process called the due date process which models the times at which these tasks are completed. Our main concern is the deviation of the completion times from the planned times. We derive conditions under which this process is stable. An interesting application of the due date process is to represent arrival processes associated with the assembly queue in manufacturing. Under this formulation, it is easy to characterize the transient and steady state behavior of the assembly queue. We also characterize a single server, exponential service queueing problem in which the arrivals are from a due date process.
52 citations
TL;DR: In this paper, if an underlying Markovian state-space system for the controlled process is available, and if this process possesses stationary transition probabilities, then the powerful ergodic theory of Markov processes may be applied.
Abstract: The principal techniques used up to now for the analysis of stochastic adaptive control systems have been 1) super-martingale (often called stochastic Lyapunov) methods and 2) methods relying upon the strong consistency of some parameter estimation scheme. Optimal stochastic control and filtering methods have also been employed. Although there have been some successes, the extension of these techniques to a broader class of adaptive control problems, including the case of time-varying parameters, has been difficult. In this paper a new approach is adopted: if an underlying Markovian state-space system for the controlled process is available, and if this process possesses stationary transition probabilities, then the powerful ergodic theory of Markov processes may be applied. Subject to technical conditions, such as stability, one may deduce 1) the existence of an invariant measure for the process and 2) the convergence almost surely of the sample averages of a function of the state process (and of its expectation) to its conditional expectation. The technique is illustrated by an application to a previously unsolved problem involving a linear system with unbounded random time-varying parameters.
49 citations
Book•
27 Feb 1987
TL;DR: In this article, the authors present a self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems, such as diffusion theory, which is a natural generalization of the flow generated by a vector field.
Abstract: This book is based on a course given at Massachusetts Institute of Technology It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems The central theme is the theory of diffusions In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields
37 citations
TL;DR: The diffusion rate of a first purchase diffusion model is interpreted as the intensity function of a counting process and Parameter estimation procedures are considered and some generalizations of the basic model are discussed.
Abstract: The diffusion rate of a first purchase diffusion model is interpreted as the intensity function of a counting process. Parameter estimation procedures are considered and some generalizations of the...
TL;DR: This paper deals with the problem of determining the possible states of a stochastic dynamic system with known outputs, provided it is in a certain causal relationship with another stochastically dynamic system whose states are given.
Abstract: This paper deals with the problem of determining the possible states of a stochastic dynamic system $S_1 $ with known outputs, provided it is in a certain causal relationship with another stochastic dynamic system $S_2 $ whose states (or some information about them) are given.
TL;DR: In this paper, the equivalence between the stationarity condition of an N -dimensional stochastic process, defined as the solution of a generalized Langevin equation with random initial values, with the fluctuation-dissipation theorem was demonstrated.
Abstract: A demonstration is given of the equivalence between the stationarity condition of an N -dimensional stochastic process a (t) , defined as the solution of a generalized Langevin equation with random initial values, with the (“second”) fluctuation-dissipation theorem. As a result, it is shown that a similar relation also holds for any stochastic process obtained as a projection of a (t) into a subspace of the original space.
TL;DR: In this article, a model of interacting biological populations, with birth and death rates depending on the population size, is studied in the quasi-stationary state, and confidence regions in the state space are constructed by a new method for the numerical, solution of the ray equations.
TL;DR: In this paper, a rigorous treatment of the optimal control problem for a continuous-time stochastic model with an infinite-horizon quadratic cost function, under weaker assumptions concerning the white-noise innovations than have been made in the literature on this subject is provided.
01 Sep 1987
TL;DR: The developed approximation depends only on the first two statistical moments of the random inputs and up to the third derivatives of the cost functions and elucidates the stochastic optimization problem yielding insights which cannot be easily obtained from the numerical application of discrete DP.
Abstract: A new approximate method of solution for stochastic optimal control problems with many state and control variables is introduced. The method is based on the expansion of the optimal control into the deterministic feedback control plus a caution term. The analytic, small-perturbation calculation of the caution term is at the heart of the new method. The developed approximation depends only on the first two statistical moments of the random inputs and up to the third derivatives of the cost functions. Its computational requirements do not exhibit the exponential growth exhibited by discrete stochastic DP and can be used as a suboptimal solution to problems for which application of stochastic DP is not feasible. The method is accurate when the cost-to-go functions are approximately cubic in a neighbourhood around the deterministic trajectory whose size depends on forecasting uncertainty. Furthermore, the method elucidates the stochastic optimization problem yielding insights which cannot be easily obtained from the numerical application of discrete DP.
TL;DR: In this paper, a canonical stochastic dynamical system for time-symmetric semimartingales is formulated by the Stochastic least-action principle in a new calculus of variations, and the phase factor of the wave function plays the role of a generating function of the canonical transformation.
Abstract: A canonical stochastic dynamical system for time‐symmetric semimartingales is formulated by the stochastic least action principle in a new stochastic calculus of variations. A certain class of stochastic dynamical systems gives a Hamiltonian formalism of Nelson’s stochastic mechanics. In a manner analogous to classical mechanics, the notions of a stochastic Poisson bracket and canonical transformation are introduced to the stochastic dynamical systems. It is shown that the phase factor of the wave function plays the role of a generating function of the canonical transformation.
TL;DR: In this article, the meaning of stochastic integrals was studied when the integrator is a quantum process which is not quite a martingale, in that it obeys estimates of the type advocated by McShane in the classical case.
TL;DR: Numerical results to illustrate the difference between deterministic and stochastic models are presented and some areas for further work are pointed out.
Abstract: This paper reviews recent developments in the field of stochastic combat models. A simple heterogeneous model with attrition rates dependent on the number of surviving forces is considered as a Markov process. Various characteristics of system dynamics are evaluated and expressed in explicit form. Numerical results to illustrate the difference between deterministic and stochastic models are presented. Some areas for further work are pointed out.
TL;DR: In this paper, nonlinear diffusions on bounded intervals perturbed by gaussian white noise are considered, and expressions for the mean and covariance and spectral density are derived for the Gaussian mean to order ϵ 2 and ϵ 3, respectively.
TL;DR: Two limit theorems related to population biology are proved and a problem of continuous time approximations for discrete time models in random environments is discussed.
Abstract: We consider a sequence of discrete parameter stochastic processes defined by solutions to stochastic difference equations. A condition is given that this sequence converges weakly to a continuous parameter process defined by solutions to a stochastic ordinary differential equation. Applying this result, two limit theorems related to population biology are proved. Random parameters in stochastic difference equations are autocorrelated stationary Gaussian processes in the first case. They are jump-type Markov processes in the second case. We discuss a problem of continuous time approximations for discrete time models in random environments.
02 Jan 1987
TL;DR: This paper presents the functional relationship between theistics of the random number generator and the statistics of the continuous random process for simulations using two commonly employed integration methods.
Abstract: Physical systems often contain subsystems that are "best" model ed as continuous random processes. When these processes are included in digital simulations, the statistics of the random num ber generator used in the simulation must be selected such that the continuous random process is modeled faithfully. In general the statistics of the random number generator will be drastically different from the statistics of the continuous random process. This paper presents the functional relationship between the sta tistics of the random number generator and the statistics of the continuous random process for simulations using two commonly employed integration methods.
TL;DR: In this paper, a chance constrained model and a model for probability maximization are formulated for the investment planning problem of risky projects, and a sequential stochastic decision making process is formulated and analyzed.
TL;DR: In this paper, a review of recent developments in the stochastic comparison of order statistics is presented, and applications to reliability problems are presented illustrating the use and value of the theoretical results described.
Abstract: This paper reviews recent developments in the stochastic comparison of order statistics. The results discussed are basically: (l) Stochastic comparisons of linear combinations of order statistics from distributions F and G where G−1 F is convex or starshaped. (2) Stochastic comparisons of individual order statistics and of vectors of order statistics from underlying heterogeneous distributions by the use of majorization and Schur function theory. (3) Stochastic comparison of random processes. Applications to reliability problems are presented illustrating the use and value of the theoretical results described
TL;DR: In this article, the authors established a stochastic integration by parts formula in which both the integrator and the integrand are elements of the two-parameter Wiener space.
Abstract: We establish a stochastic integration by parts formula in which both the integrator and the integrand are elements of two-parameter Wiener (or Yeh–Wiener) space. We also establish the continuity of the stochastic integral with respect to binary quadratic approximation.
TL;DR: In this paper, various general perturbational schemes for continuous stochastic equations are considered, which have many analogous features with the iterational solution of Schwinger equation for S-matrix.
Abstract: The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probaibility distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes. stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion - controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and nonequilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered.
01 Jan 1987
TL;DR: Three types of efficient sequential estimation functions in a class of continuous time stochastic population models are discussed and their asymptotic behaviour is investigated.
Abstract: Sequential, i.e., randomly stopped estimation functions in a class of continuous time stochastic population models are considered. The class includes finite, irreducible Markov processes. Three types of efficient sequential estimation functions are discussed and their asymptotic behaviour is investigated. The main tools of analysis are taken from point process theory.
TL;DR: In this paper, the validity of a NSCOMBE-type condition for special stochastic processes in a BANACH space was investigated, and it was shown that the condition is useful for proving limit theorems of randomly indexed sums.
Abstract: This paper treats the validity of A NSCOMBE-type conditions for special stochastic processes in a BANACH space. Such conditions concern the uniform continuity of sequences of stochastic processes and are useful for proving limit theorems of randomly indexed sums. The first part is devotes to stochastic processes with independent increments. The second part investigates stochastic processes generated by operator normed sums of weakly dependent random variables (strongly mixing or unigorm;y strongly mixing). The special case of operator normed sums of independent random varables in an EUCLIDEAN space was treated in GLESER [4], but these results are incorrect.