The definition to the term "Stochastic Process" is: A statistical process involving a number of random variables depending on a number variable. Which in most cases, is time.
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Stochastic means non-deterministic. This means that something contains an inherent degree of randomness. For more detail, you should consult a dictionary or more detailed literature on probability theory.
Mathematical model is exact in nature.it has Beta zero and Beta one and no stochastic or disturbance variables. Econometric model represents omitted variable, error in measurement and stochastic variables.
A Stochastic error term is a term that is added to a regression equation to introduce all of the variation in Y that cannot be explained by the included Xs. It is, in effect, a symbol of the econometrician's ignorance or inability to model all the movements of the dependent variable.
A stochastic error is a type of random error that occurs in statistical models or experiments. It is caused by factors that are unpredictable or beyond the control of the researcher, leading to variability in the data. Stochastic errors can be minimized through larger sample sizes or by using statistical techniques to account for their presence in the analysis.
Regression analysis is based on the assumption that the dependent variable is distributed according some function of the independent variables together with independent identically distributed random errors. If the error terms were not stochastic then some of the properties of the regression analysis are not valid.