Let (X 0 ) be uniformly distributed over ( 0, T , X 1 ) be uniformly distributed over ( left 0, X 0 ight ), and, generally, (X i 1 ) be uniformly distributed over ( left 0, X i ight , i 0,1, ldots ) Verify The sequence ( left X 0 , X 1 , ldots ight ) is a supermartingale with (E left(X k ight) frac...

Let (X_{0}) be uniformly distributed over ([0, T], X_{1}) be uniformly distributed over (left[0, X_{0} ight]), and,

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Let $X_{0}$ be uniformly distributed over $[0, T], X_{1}$ be uniformly distributed over $\left[0, X_{0}\right]$, and, generally, $X_{i+1}$ be uniformly distributed over $\left[0, X_{i}\right], i=0,1, \ldots$.

Verify: The sequence $\left\{X_{0}, X_{1}, \ldots\right\}$ is a supermartingale with $E\left(X_{k}\right)=\frac{T}{2^{k+1}} ; k=0,1, \ldots$

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Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

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Let (X_{0}) be uniformly distributed over ([0, T], X_{1}) be uniformly distributed over (left[0, X_{0} ight]), and,

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