Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.

Systems with finite communication bandwidth constraints. I. State estimation problems

Abstract: In this paper, we investigate a state estimation problem involving finite communication capacity constraints. Unlike classical estimation problems where the observation is a continuous process corrupted by additive noises, there is a constraint that the observations must be coded and transmitted over a digital communication channel with finite capacity. This problem is formulated mathematically, and some convergence properties are defined. Moreover, the concept of a finitely recursive coder-estimator sequence is introduced. A new upper bound for the average estimation error is derived for a large class of random variables. Convergence properties of some coder-estimator algorithms are analyzed. Various conditions connecting the communication data rate with the rate of change of the underlying dynamics are established for the existence of stable and asymptotically convergent coder-estimator schemes.

Diffusion processes in one dimension

Abstract: in a finite or infinite interval r1

On circularity

Abstract: Circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors. However, this concept can be extended in various ways for nonnormal vectors. The first purpose of the paper is to introduce and compare some possible definitions of circularity. From these definitions, it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components. Therefore, the relationships between circularity and stationarity are analyzed in detail. Finally, the theory of linear mean square estimation for complex signals exhibits some connections with circularity, and it is shown that without this assumption, the estimation theory must be reformulated. >

Probability and statistics in engineering and management science

Abstract: Introduction and Data Description An Introduction to Probability One-Dimension Random Variables Functions of One Random Variable and Expectation Joint Probability Distributions Some Important Discrete Distributions Some Important Continuous Distributions The Normal Distribution Random Samples and Sampling Distributions Parameter Estimation Tests of Hypotheses Design and Analysis of Single-Factor Experiments: The Analysis of Variance Design of Experiments with Several Factors Simple Linear Regression and Correlation Multiple Regression Nonparametric Statistics Statistical Quality Control and Reliability Engineering Stochastic Processes and Queueing Statistical Decision Theory References Appendix Answers to Selected Exercises Index.