Occupation-times formula

For a continuous semimartingale

X

with local time of a semimartingale

L_{t}^{a} (X)

,

\int_{0}^{t} f (X_{s}) d [X]_{s} = \int_{R} f (a) L_{t}^{a} (X) d a

for every nonnegative measurable function

f

.

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Brownian occupation time

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