ABSTRACT
This chapter contains some necessary preliminary notions and facts associated with separable Banach spaces, including random (or stochastic) processes, stochastic integration, martingales and martingale problems, weak convergence and semigroup theory. It gives a few examples of semigroups of operators and generators and mentions that a semi-Markov process does not generate a semigroup due to the arbitrary distribution function for the sojourn times, rather than the exponential one in the case of a Markov process.
