Stochastic Mathematical Modelling

Stochastic mathematical modelling is, together with transfer phenomena and statistical approaches, a powerful technique, which can be used in order to have a good knowledge of a process without much tedious experimental work. The principles for establishing models, which were described in the preceding chapter, are still valuable. However, they will be particularized for each example presented below. 

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For the mathematical models based on transport phenomena as well as for the stochastic mathematical models, we can introduce new grouping criteria. When the basic process variables (species conversion, species concentration, temperature, pressure and some non-process parameters) modify their values, with the time and spatial position inside their evolution space, the models that describe the process are recognized as models with distributed parameters. From a mathematical viewpoint, these models are represented by an assembly of relations which contain partial differential equations The models, in which the basic process variables evolve either with time or in one particular spatial direction, are called models with concentrated parameters. 

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