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Unformatted text preview: uence of σalgebras, ℱ ⊂ ℱ
a. (5 points)
Let be a random variable whose values belong to
. Prove that
is a sequence of integrable random variables, i.e.
b. (7 points)
Let τ be a stopping time with respect to ℱ . Prove that the following
c. (6 points)
is adapted. Let
monotone increasing sequence of stopping-times with respect to ℱ so
∞, a.s. Use part b to show that if
supermartingale for each n, then
is a supermartingale as
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This document was uploaded on 03/01/2014 for the course STATS 400 at Michigan State University.
- Spring '12