“Σ-Algebra of τ-past”的意思、由来-开放百科全书

词条

Σ-Algebra of τ-past

释义

Definition
Properties
Monotonicity Measurability
References

The σ-algebra of τ-past, (also named stopped σ-algebra, stopped σ-field, or σ-field of τ-past) is a σ-algebra associated with a stopping time in the theory of stochastic processes, a branch of probability theory.^[1]^[2]

Definition

Let be a stopping time on the filtered probability space . Then the σ-algebra

is called the σ-algebra of τ-past.^[1]^[2]

Properties

Monotonicity

Is are two stopping times and

almost surely, then

Measurability

A stopping time is always -measurable

References

^[1]^[2]

2 : Stochastic processes|Set families

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