Localization and Approximation

Abstract

Stochastic integral processes will be constructed by approximation. One first defines the integral process in a straightforward manner for elementary integrands. Then one shows that the approximation of more general integrands by elementary ones yields a convergent sequence of the corresponding integral processes. The details depend on the choice of the respective spaces and concepts of convergence. In this chapter we discuss the part of the arguments which can be formulated without explicit reference to stochastic integrals. If you have ploughed through this somewhat technical chapter the way to the stochastic integral is open.