Abstract
In this chapter, we introduce the reader to the basic operators of Malliavin calculus. This is because, in the next chapter, we shall use this framework to study the convergence in law of some functionals involving fractional Brownian motion. For the sake of simplicity and to avoid useless technicalities, we only consider the case where the underlying Gaussian process, fixed once for all, is a two-sided classical Brownian motion W = (W t ) t∈ℝ (see (1.8)) defined on some probability space (Ω, ℱ, P); we further assume that the σ-field ℱ is generated by W.
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- 1.
Any adapted process u that is either càdlàg or càglàd admits a progressively measurable version. We will always assume that we are dealing with it, meaning that the restriction of u to the product (-∞, t] × Ω is ℬ ((-∞, t]) ⊗ ℱ t -measurable for all t.
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© 2012 Springer-Verlag Italia
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Nourdin, I. (2012). Malliavin Calculus in a Nutshell. In: Selected Aspects of Fractional Brownian Motion. B&SS — Bocconi & Springer Series. Springer, Milano. https://doi.org/10.1007/978-88-470-2823-4_5
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DOI: https://doi.org/10.1007/978-88-470-2823-4_5
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2822-7
Online ISBN: 978-88-470-2823-4
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