Probability and Stochastic Processes
Yuriy S. Shmaliy, Shunyi Zhao · 2022
This chapter provides a brief introduction to the concepts and foundations of the theory of probability and stochastic processes and methods of state estimation. A collection of random variables sets up some random process. Two kinds of special characteristics called moments have found applications in the representation of random variables: raw (ordinary) moments and central moments. Spectral analysis of random processes in the frequency domain plays the same role as correlation analysis in the time domain. As a collection of Gaussian variables, a Gaussian process is a stochastic process whose variables have a multivariate normal distribution. Dynamic physical processes can be both linear and nonlinear with respect to variables and perturbations. Probability theory and methods developed for stochastic processes play a fundamental role in understanding the features of physical processes driven and corrupted by noise.