A 'stochastic' process is a 'random' or 'conjectural' process, and this book is concerned with applied probability and statistics. Whilst maintaining the mathematical rigour this subject requires, it addresses topics of interest to engineers, such as problems in modelling, control, reliability maintenance, data analysis and engineering involvement with insurance.This book deals with the tools and techniques used in the stochastic process – estimation, optimisation and recursive logarithms – in a form accessible to engineers and which can also be applied to Matlab. Amongst the themes covered in the chapters are mathematical expectation arising from increasing information patterns, the estimation of probability distribution, the treatment of distribution of real random phenomena (in engineering, economics, biology and medicine etc), and expectation maximisation. The latter part of the book considers optimization algorithms, which can be used, for example, to help in the better utilization of resources, and stochastic approximation algorithms, which can provide prototype models in many practical applications.*An engineering approach to applied probabilities and statistics *Presents examples related to practical engineering applications, such as reliability, randomness and use of resources*Readers with varying interests and mathematical backgrounds will find this book accessible
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Yes, you can access Stochastic Processes by Kaddour Najim,Enso Ikonen,Ait-Kadi Daoud in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.
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:
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, and gives several examples of stochastic processes such as random walk, Markov chains, renewal processes and martingales. We also present the properties of martingale processes and a set of convergence theorems. The next section presents the main tools related to probability theory.
1.2. Foundations of Probability
Let us recall some results related to the algebra sets. The main operations on sets are “and”, “or” or “+”, and “not”, which are denoted by ∩, ∪
