Stochastic Calculus Part I

Raymond H. Chan, Yves ZY. Guo, Spike T. Lee and Xun Li
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Raymond H. Chan: City University of Hong Kong
Yves ZY. Guo: BNP Paribas CIB
Spike T. Lee: The Chinese University of Hong Kong
Xun Li: The Hong Kong Polytechnic University

Chapter Chapter 10 in Financial Mathematics, Derivatives and Structured Products, 2019, pp 103-118 from Springer

Abstract: Abstract The σ-algebra generated by a random variable X, denoted σ(X), is the σ-algebra by the collection of {X ∈ B} (i.e. {ω : X(ω) ∈ B}), where B is any interval in ℝ $${\mathbb {R}}$$ . Let G $$\mathcal {G}$$ be a σ-algebra on Ω. Then X is said to be G $$\mathcal {G}$$ -measurable Measurable if σ ( X ) ⊆ G $$\sigma (X) \subseteq \mathcal {G}$$ .

Date: 2019
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DOI: 10.1007/978-981-13-3696-6_10

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