TABLE OF CONTENTS In this chapter an introduction to the basic concepts and properties of stochastic processes is given. Stochastic processes play an important role in various fields (chemistry, process engineering, reliability, maintenance, biology, medicine, economy, insurance, etc.). Ermoliev and Wets [20] say:
| Note | Systems involving interactions between man, nature and technology are subject to disturbance which may be unlike anything which has been experienced in the past. In particular, the technological revolution increases uncertainty as each new stage perturbs existing structures, limitations and constraints. |
For example, the combination of a hazard and operability study and a fault tree analysis gives the probability of an accident occurring in a chemical system. Other examples can be drawn from chemical engineering. Due to random occurrences of molecular collision, complexations and dissociations, chemical processes exhibit a stochastic behavior [15]. It has been observed that in a fluidized bed the conversion rate was higher than in a rotating kiln; or in a steady layer. Based on the available models, it was impossible to explain these phenomena. In order to explain these phenomena, the virtual rate constant was assumed to be a stochastic variable distributed according to the uniform law, by Blickle et al. [9]. Stochastic models are used to represent the randomness and to provide estimates of the media parameters that determine fluid flow, pollutant transport, and heat-mass transfer in natural porous media. Indeed, the pore structure in these media is very complex [41].
This chapter presents the foundations of probability, discrete stochastic processes,...
