ABSTRACT
A stochastic model is a mathematical model of a real-world process or potentially new real-world process, where at least one variable is uncertain or random. This chapter outlines the properties of a generic stochastic model. It introduces the nature and goals of stochastic level crossing method (LC). LC utilizes “SP rate balance” across state-space levels or boundaries, to build the integral equation for the probability density function (pdf), term by term. LC utilizes sample paths as “concrete templates” for building “analytic integral equations” for the pdfs of the key random variables (r.v.) in a stochastic model, by inspection. LC provides an intuitive, efficient method of analysis, which mitigates a significant amount of time-consuming algebra. Basic LC theorems connect level-crossing rates of the “physical” sample path of the r.v. of interest, to corresponding “analytic” terms of an integral equation, whose solution is the analytic pdf of the r.v.
