Basics of Stochastic Processes
In the literature the generalized random experiments are frequently called random functions. In engineering, science, and economics there are many time-dependent random phenomena which can be modeled by stochastic processes: In an electrical circuit it is not possible to keep the voltage strictly constant. Random fluctuations of the voltage are for instance caused by thermal noise. Both meteorological and industrial noise create electrical discharges in the atmosphere which occur at random time points with randomly varying intensity. 'Classic' applications of stochastic processes in economics are modeling the fluctuations of share prices, rendits, and prices of commodities over time. Important impulses for the development and application of stochastic processes came from biology: stochastic models for population dynamics from cell to mammal level, competition models, capture-recapture models, growth processes, and many more. The purely random sequence is the most popular discrete-time stochastic process for modelling a random noise, which superimposes an otherwise deterministic time-dependent phenomenon.