Showing papers on "Stochastic simulation published in 1992"

Random Field Models in Earth Sciences

Abstract: Prolegomena the spatial random field model the intrinsic spatial random field model the factorable random field model the spatiotemporal random field model space transformations of random fields random field modelling of natural processes simulation of natural processes estimation in space and time sampling design.

A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation

Abstract: Bird's direct simulation Monte Carlo method for the Boltzmann equation is considered. The limit (as the number of particles tends to infinity) of the random empirical measures associated with the Bird algorithm is shown to be a deterministic measure-valued function satisfying an equation close (in a certain sense) to the Boltzmann equation. A Markov jump process is introduced, which is related to Bird's collision simulation procedure via a random time transformation. Convergence is established for the Markov process and the random time transformation. These results, together with some general properties concerning the convergence of random measures, make it possible to characterize the limiting behavior of the Bird algorithm.

Regenerative Stochastic Simulation

Abstract: Preface. Discrete-Event Simulations. Regenerative Stochastic Processes. Regenerative Simulation. Networks of Queues. Passage Times. Simulations With Simultaneous Events. Appendix A. Limit Theorems for Stochastic Processes. Appendix B. Random Number Generation.

The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations

Abstract: : We establish general conditions for the asymptotic validity of sequential stopping rules to achieve fixed-volume confidence sets for simulation estimators of vector-valued parameters. The asymptotic validity occurs as the prescribed volume of the confidences set approaches zero. There are two requirements: a functional central limit theorem for the estimation process and strong consistency (with-probability-one convergence) for the variance or scaling matrix estimator. Applications are given for: sample means of i.i.d. random variables and random vectors, nonlinear functions of such sample means, jackknifing, Kiefer-Wolfowitz and Robbins-Monro stochastic approximation, and both regenerative and non-regenerative steady-state simulation. Keywords: Stochastic simulation, Variance estimators.

Discrete Event Simulation: A Practical Approach

Abstract: BASIC CONCEPTS AND TERMINOLOGY. Concept of a System. System Methodology. Advantages and Disadvantages of Simulation. Simulation Terminology. PROBABILITY CONCEPTS IN SIMULATION. Probability. Set Theory, Compound Events. Conditional Probability, Independent Events. Discrete Distributions. Continuous Distributions. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Functions of a Random Variable. Moments. Generating Functions. Multivariate Distributions. DETAILED ANALYSIS OF COMMON PROBABILITY DISTRIBUTIONS. Bernoulli Distribution. Binomial Distribution. Geometric Distribution. Poisson Distribution. Uniform Distribution. Normal Distribution. Exponential Distribution. Chi-Square Distribution. Student's t-Distribution. F-Distribution. STATISTICS AND RANDOM SAMPLES. Descriptive Statistics and Frequency Diagrams. Statistics and Sampling Distributions. Method of Least Squares. Estimation. Confidence Interval Estimates. STATISTICAL TESTS. Tests of Hypotheses. Student's t-Test. The F-Test. The Chi-Square Goodness-of-Fit Test. The Kolmogorov-Smirnov Test. GENERATION OF RANDOM NUMBERS. Pseudorandom Numbers. Algorithms for Generating Pseudorandom Numbers. Testing and Validating Pseudorandom Sequences. Generation of Nonuniform Variates. DISCRETE SYSTEM SIMULATION. Simulation Terminology. Time Management Methods. Object Generation. Queue Management and List Processing. Collecting and Recording Simulation Data. MODEL VALIDATION. Evaluation of the Simulation Model. Validation Description. Sampling Methods. THE DESIGN OF SIMULATION EXPERIMENTS. Completely Randomized Design. Randomized Complete Block Design. Factorial Design. Network Simulation Model Performance Analysis. ESTIMATION OF MODEL PARAMETERS. Optimization of Response Surfaces. Heuristic Search. Complete Enumeration. Random Search. Steepest Ascent (Descent). Coordinate or Single-Variable Search. Parallel Tangent Search. Conjugate Direction Search. OUTPUT ANALYSIS. Analysis of Simulation Results. Estimation and Confidence Limits. Initial Conditions and Inputs. Simulation Model Run Length. Variance Reduction. LANGUAGES FOR DISCRETE SYSTEM SIMULATION. Language Characteristics. Use of Multipurpose Languages. Simulation Languages. DISTRIBUTED SIMULATION. The System Simulation Problem. Decomposition of a Simulation. Synchronization of Distributed Model Components. Deadlock Resolution in Distributed Simulations. QUEUEING THEORY AND SIMULATION. Review of the Poisson and Exponential Distributions. The M/M/1/8/FIFO System. Summary Measures for the M/M/1/8/FIFO System. The M/M/1/K/FIFO System. The M/M/C/8/FIFO System. Priority Queueing Systems. APPENDIX TABLES. Normal Distribution Function. Student's t-Distribution Function. Chi-Square Distribution Function. F-Distribution Function. Poisson Distribution Function. Critical Values for the Kolmogorov-Smirnov Test. INDEX.

A nonlinear disaggregation method with a reduced parameter set for simulation of hydrologic series

Abstract: A multivariate dynamic disaggregation model is developed as a stepwise approach to stochastic disaggregation problems, oriented toward hydrologic applications. The general idea of the approach is the conversion of a sequential stochastic simulation model, such as a seasonal AR(1), into a disaggregation model. Its structure includes two separate parts, a linear step-by-step moments determination procedure, based on the associated sequential model, and an independent nonlinear bivariate generation procedure (partition procedure). The model assures the preservation of the additive property of the actual (not transformed) variables. Its modular structure allows for various model configurations. Two different configurations (PAR(1) and PARX(1)), both associated with the sequential Markov model, are studied. Like the sequential Markov model, both configurations utilize the minimum set of second-order statistics and the marginal means and third moments of the lower-level variables. All these statistics are approximated by the model with the use of explicit relations. Both configurations perform well with regard to the correlation of consecutive lower-level variables each located in consecutive higher-level time steps. The PARX(1) configuration exhibits better behavior with regard to the correlation properties of lower-level variables with lagged higher-level variables. 27 refs., 5 figs., 3 tabs.

A random number generator based on the logit transform of the logistic variable

Abstract: A nonperiodic random number generator, which is based on the logistic equation, is presented. A simple transformation that operates on the logistic variable and leads to a sequence of random numbers with a near‐Gaussian distribution, is described and discussed. The associated algorithm can be easily utilized in laboratory exercises, classroom demonstrations, and software written for stochastic modeling purposes.

Nonlinear Stochastic Evolution Problems in Applied Sciences

Abstract: Preface. 1. Stochastic Models and Random Evolution Equations. 2. Deterministic Systems with Random Initial Conditions. 3. The Random Initial Boundary Value Problem. 4. Stochastic Systems with Additional Weighted Noise. 5. Time Evolution of the Probability Density. 6. Some Further Developments of the SAI Method. Appendix: Basic Concepts of Probability Theory and Stochastic Processes. Authors Index. Subject Index.

Application of stochastic simulation to climatic-change studies

Abstract: Stochastic modelling provides a tool for exploring the full implications of the statistical behavior of historical records and can be used to predict the changing probabilities that events of various magnitudes will occur for different climatic change scenarios. Two simulation models are presented, one for daily air temperature, and the other for daily precipitation. The simulation procedures are: (1) extract salient parameter values from historical records; (2) simulate long sequences of data using the stochastic models, with or without a climatic change scenario as provided by a general circulation model; and (3) using the simulated data as inputs, derive the probability distributions of other variables based on known deterministic or probabilistic relationships between the input and the predicted variables.

Distributed random number generation

Abstract: In a functional program, a simple random number generator may generate a lazy list of random numbers. This is fine when the random numbers are consumed sequentially at a single point in the program. However, things are more complicated in a program where random numbers are used at many locations, such as in a large simulation. The programmer should not need to worry about providing separate generators with a unique seed at each point where random numbers are used. At the same time, the programmer should not need to coordinate the use of a single stream of random numbers in many parts of the program, which can be particularly difficult with lazy evaluation or parallel processing.We discuss several techniques for distributing random numbers to various parts of a program, and some methods of allowing different program components to evaluate random numbers locally. We then propose a new approach in which a random number sequence can be split at a random point to produce a pair of random number sequences that can be used independently at different points in the computation.The approach can also be used in distributed procedural programs, where it is desirable to avoid dealing with a single source of random numbers. The approach has the added advantage of producing repeatable results, as might be needed in debugging, for example.

Structured Biological Modelling: a method for the analysis and simulation of biological systems applied to oscillatory intracellular calcium waves.

Abstract: In biology signal and information processing networks are widely known. Due to their inherent complexity and non-linear dynamics the time evolution of these systems can not be predicted by simple plausibility arguments. Fortunately, the power of modern computers allows the simulation of complex biological models. Therefore the problem becomes reduced to the question of how to develop a consistent mathematical model which comprises the essentials of the real biological system. As an interface between the phenomenological description and a computer simulation of the system the proposed method of Structured Biological Modelling (SBM) uses top-down levelled dataflow diagrams. They serve as a powerful tool for the analysis and the mathematical description of the system in terms of a stochastic formulation. The stochastic treatment, regarding the time evolution of the system as a stochastic process governed by a master equation, circumvents most difficulties arising from high dimensional and non-linear systems. As an application of SBM we develop a stochastic computer model of intracellular oscillatory Ca2+ waves in non-excitable cells. As demonstrated on this example, SBM can be used for the design of computer experiments which under certain conditions can be used as cheap and harmless counterparts to the usual time-consuming biological experiments.

Simulation and approximation of stochastic processes by spline functions

Abstract: Error bounds for simultaneous approximation of stochastic processes by means of spline functions are derived. As opposed to conventional methods, conditions such as regularity of covariances, stationarity, continuity of sample paths, etc. can be dropped, and the error bounds are valid with respect to arbitrary norms. Several applications are indicated: simulating solutions of some stochastic differential equations, computing distributions of continuous functionals by simulation as well as interpolation, numerical differentiation, and numerical integration of stochastic processes by splines.

Burger's model of turbulence as a stochastic process

Abstract: A recently proposed mesoscopic description of fluid dynamics leads to a new approach to turbulence. In contrast to the classical statistical theory of turbulence the new approach introduces a probabilistic time evolution of the random velocity governed by a master equation. The mesoscopic approach is explained by means of the (1+1)-dimensional Burger's model of turbulence. By a continuous time stochastic simulation, realizations of turbulent velocity fields are generated. Correlation functions and energy spectra are evaluated from appropriate ensemble averages.

Determining design gust loads for nonlinear aircraft similarity between methods based on matched filter theory and on stochastic simulation

Abstract: This is a work-in-progress paper. It explores the similarity between the results from two different analysis methods - one deterministic, the other stochastic - for computing maximized and time-correlated gust loads for nonlinear aircraft. To date, numerical studies have been performed using two different nonlinear aircraft configurations. These studies demonstrate that results from the deterministic analysis method are realizable in the stochastic analysis method.

The Use of Stochastic Simulation in Knowledge‐Based Systems

Abstract: Knowledge-based systems support the decision-making process with the help of domain specific knowledge bases The knowledge bases almost always have uncertainty associated with them A variety of approaches have been proposed in the artificial intelligence (AI) literature for the construction of and reasoning with uncertain knowledge bases Building on this stream of research, we focus on how stochastic simulation can be used to construct and reason with knowledge bases that have uncertainties An advantage of the simulation methodology is that it may not have to make many of the assumptions made by other approaches It also allows the designer of the knowledge-based system to control the methodology based on accuracy and time requirements The simulation approach to knowledge base construction is a modified version of the concept induction procedure used in AI However, it incorporates, as does simulation modeling, statistical tests to identify the best rule that describes the relationship among the variables We show that when simulation is used to reason with uncertain knowledge bases, under certain conditions, the number of simulation trials needed to achieve a given level of accuracy is independent of the characteristics, such as the size, of the knowledge base Empirical results obtained from an experiment confirm our theoretical results and provide evidence that simulation methodology is practical for real life knowledge-based systems

Deterministic Pseudo-Annealing: Optimization in Markow-Random-Fields. An Application to Pixel Classification

Abstract: We present in this paper a new deterministic and massively parallel algorithm for combinatorial optimization in a Markov Random Field. This algorithm is an extension of previous relaxation labeling by optimization algorithms. First, the a posteriori probability of a tentative labeling, defined in terms of a Markov Random Field is generalized to continuous labelings. This merit function of probabilistic vectors is then convexified by changing its domain. Global optimization is performed, and the maximum is tracked down while the original domain is restaured. On an application to contextual pixel quantization, it compares favorably to recent stochastic (simulated annealing) or deterministic (graduated non-convexity) methods popularized for low-level vision.

Weak convergence of approximate solutions of random equations

Abstract: Approximations of random operator equations are considered where the stochastic inputs and the underlying deterministic equation are approximated simultaneously. The main convergence result asserts that, under reasonable and verifiable assumptions, a sequence of weak solutions of approximate random equations converges weakly to a weak solution of the original equation. It is shown that this theorem extends and unifies results already known. We apply our theory to approximations of random differential equations involving stochastic processes with discontinuous paths and to projection methods for nonlinear random Hammerstein integral equations in spaces of integrable functions.

Optimal Discretization of Random Fields for SFEM

Abstract: A new method for discretization of random fields (representation in terms of random variables) is introduced based on the principle of optimal linear estimation theory. The method is more efficient than other existing methods; i.e., for the same level of accuracy it requires a smaller number of random variables to describe the field. The method is particularly relevant for application in stochastic finite element problems.

Stochastic Simulation in Mixed Graphical Association Models

Abstract: The application of stochastic simulation to mixed graphical association models enables us not only to estimate the marginal probabilities, means and variances of the variables, but also to estimate the marginal densities of continuous variables.

On the Distribution of the Maximum of a Random Number of Random Variables

Abstract: We present a correct estimate of the rate of convergence and asymptotic expansions in the limit theorem for a sample maximum of random variables till the stopping time.

A distribution-free random number generator via a matrix-exponential representation

Abstract: The recently conceived Matrix-Exponential distribution is dense in the set of all real, continuous, nondecreasing functions whose domain is in the half-open interval [0,-). To define a distribution function, only two parameters am tequirad: (1) a vector p and (2) a matrix B. The singular form of the function permit applications that use a diverse set of distributions to be sirnplifkd into a single module whose input arguments are p and B. Random number generation will be examined as an application for the Matrix-Exponential function; with the restriction that evaluation of the function be performed on fried precision numeric software. To assess the practicality of the implementation, a naive approach will be introrhmd and several distribution functions will be surveyed.

Simulation of Random Variables and Random Processes

Abstract: In electrical systems we use voltage or current waveforms as signals for collecting, transmitting, and processing information, as well as for controlling and providing power to a variety of devices. Signals, whether they are voltage or current waveforms, are functions of time and they can be classified as deterministic or random. Deterministic signals can be described by functions in the usual mathematical sense with time t as the independent variable. In contrast to a deterministic signal, a random signal always has some element of uncertainty associated with it, and hence it is not possible to determine its value with certainty at any given point in time.

A Simple Nonperiodic Random Number Generator: A Recursive Model for the Logistic Map

Abstract: : A nonperiodic random number generator which is based on the logistic equation is presented. A simple transformation which operates on the logistic variable and leads to a sequence of random numbers with a near-Gaussian distribution is described and discussed. The associated algorithm can be easily utilized in laboratory exercises, classroom demonstrations and software written for stochastic modelling purposes. Logistic map, Recursive process, Random number generator.