Preliminaries

Kiyosi Itô

Chapter 0 in Stochastic Processes, 2004, pp 1-38 from Springer

Abstract: Abstract Let (Ω,B,P) be the basic probability space. The family B of all sub-σ-algebras of ß is a complete lattice with respect to the usual set-theoretic inclusion relation.1 For {Bλ : λ ∈ Λ} ⊂ B the least upper bound is denoted by ⋁λ B λ and the greatest lower bound by Λλ B λ. The latter, Λλ B λ, is the same as the set-theoretic intersection ∩λ B λ but the former, ⋁λ B λ, is not the set-theoretic union ∪λ B λ but the σ-algebra generated by the union.

Keywords: Conditional Expectation; Bounded Measure; Divisible Distribution; Gauss Distribution; Compound Poisson Distribution (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-662-10065-3_1

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