Usual hypotheses

In probability theory, given a probability space $(\Omega ,{\mathcal {F}},\mathbb {P} )$ , a filtration $\mathbb {F} =\{{\mathcal {F}}_{t}\}_{t\geq 0}$ is said to satisfy the usual hypotheses if:^[1]

${\mathcal {F}}_{0}$ contains all $\mathbb {P}$ -negligible events.
$\mathbb {F}$ is right-continuous.

References

↑ Pascucci, Andrea. Pde and Martingale Methods in Option Pricing. Berlin: Springer, 2011.

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