Examples
- Any stopping time is a hitting time for a properly chosen process and target set. This follows from the converse of the Début theorem (Fischer, 2013).
- Let B denote standard Brownian motion on the real line R starting at the origin. Then the hitting time τA satisfies the measurability requirements to be a stopping time for every Borel measurable set A ⊆ R.
- For B as above, let denote the first exit time for the interval (−r, r), i.e. the first hit time for (−∞, −r] ∪ [r, +∞). Then the expected value and variance of satisfy
- For B as above, the time of hitting a single point (different from the starting point 0) has the Lévy distribution.
Read more about this topic: Hitting Time
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