Stochastic Calculus: I

Raymond H. Chan, Yves ZY. Guo, Spike T. Lee and Xun Li
Additional contact information
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 13 in Financial Mathematics, Derivatives and Structured Products, 2024, pp 137-153 from Springer

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

Date: 2024
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DOI: 10.1007/978-981-99-9534-9_13

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