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In [8] we defined and studied a class of summable processes, called additive summable processes, that is larger than the class previously studied by Dinculeanu and Brooks [2]. We also defined a stochastic integral with respect to an additive summable process and proved several properties of the integral. In this article we consider examples of processes that are integrable with respect to an additive summable process or locally integrable with respect to a locally additive summable processes. In particular, we show that if X is a locally additive summable process, then X− is integrable with respect to X. This is essential, for example, in proving an Itô formula for locally additive summable processes.

Locally integrable processes with respect to locally additive summable processes