We defined a semimartingale as a “good integrator” in Chap. II, and this led naturally to defining the stochastic integral as a limit of sums. To express an integral as a limit of sums requires some path smoothness of the integrands and we limited our attention to processes in L: the space of adapted processes with paths that are left continuous and have right limits. The space L is sufficient to prove Itô’s formula, the Girsanov-Meyer theorem, and it also suffices in some applications such as stochastic differential equations. But other uses, such as martingale representation theory or local times, require a larger space of integrands.
Weitere Kapitel dieses Buchs durch Wischen aufrufen
- General Stochastic Integration and Local Times
- Springer Berlin Heidelberg
- Chapter IV
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