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Results tagged with entropy
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user 22157
3
votes
1
answer
340
views
Example of Girsanov change of density with finite relative entropy, but with infinite integr...
If $\mathbb E^{\mathbb Q} \left[ \int_0^{\infty} \theta_t^2 \ d t \right] <\infty$, it is not hard to show (see below) that the relative entropy
$\mathcal H(\mathbb Q;\mathbb P) := \mathbb E^{\mathbb Q … I do not succeed in showing the reverse direction, i.e. that finite relative entropy implies square integrability of $(\theta_t)$, (unless $Z$ is bounded from above and below by a constant). …
- 985
2
votes
Accepted
Example of Girsanov change of density with finite relative entropy, but with infinite integr...
I can show that finite relative entropy in this setting implies $\mathbb E^{\mathbb Q} \int_0^{\infty} \theta_t^2 \ d t < \infty$. …
- 985