Usual hypotheses

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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]

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


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