Abstract
In this chapter we construct Ito’s stochastic integral (first introduced in [39]), and prove the famous Ito formula. We also establish several not quite standard versions of that formula, in particular for certain functions which do not satisfy the regularity assumptions of the basic result. In particular, we prove a d-dimensional version of the famous Tanaka formula, see Proposition 2.26 and the corollaries which follow. Those refined results will be useful later in the book. We also discuss in great detail in Sect. 2.4 a martingale representation theorem which will play an essential role in the study of BSDEs. Finally we present Girsanov’s theorem.
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