Asymptotic Statistics by Reinhard Höpfner

Author:Reinhard Höpfner [Höpfner, Reinhard]
Language: eng
Format: epub, pdf
Publisher: De Gruyter
Published: 2014-04-01T00:00:00+00:00

For statistical purposes, the filtered spaces in Definition 5.11 and Theorem 5.12 are frequently path spaces for certain classes of stochastic processes.

5.13 Notations. In dimension d ≥ 1, write C for the space of continuous functions f : [0, ∞) → ℝd equipped with the topology of locally uniform convergence, and for the Borel σ -field. At the same time, is the σ -field generated by the coordinate projections ƒ → f(t), t ≥ 0 (cf. [11], [64, Chap. VI.1]). On , we write (ηt)t ≥0 for the canonical process. i.e. the process of coordinate projections ηt(f) := f (t), t ≥ 0, f ∈ C. Let G denote the (right-continuous) filtration generated by η

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