The Basic Concepts of Random Processes and Stochastic Calculus
In this chapter we briefly give some basic probabilistic concepts and definitions of random processes such as the Markov, Gaussian and Wiener processes (see Gihman and Skorokhod, 1975; Dynkin, 1965), and therefore there is a large number of theoretically-probabilistic terms. There is a reason for introducing the terms: a ‘random variable’ and ‘random process’ for the equivalent ‘measurable function’ and a ‘random field’, namely an implied change of view-point. We use the word ‘random’ although in theoretically-probabilistic literature the words ‘random’ and ‘stochastic’ are used equally.
KeywordsBrownian Motion Characteristic Function Markov Process Random Process Transition Function
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