Construction of Lévy Processes and Their Corresponding SDEs: The Infinite Variation Case
In this chapter, we consider a class of Lévy processes which are not of bounded variation as in the preceding chapter but instead they are processes with paths of infinite variation. From the pedagogical point of view, this chapter provides the construction of the Lévy process, leaving for the reader most of the developments related to the construction of the stochastic integral, the Itô formula and the associated stochastic differential equations. This is done in the exercises in order to let you test your understanding of the subject. This is done on two levels. You will find the ideas written in words in the proofs. If you do not understand them you may try a further description that may be given in Chap. 14. It is a good exercise to try to link the words and the equations so that you understand the underlying meaning. This is also a chapter that may be used for promoting discussion between students and the guiding lecturer.