Let a discrete-time stochastic process (left{X_{0}, X_{1}, ldots ight}) be defined by [X_{n}=Y_{0} cdot Y_{1} cdots Y_{n}]

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Let a discrete-time stochastic process $\left\{X_{0}, X_{1}, \ldots\right\}$ be defined by

\[X_{n}=Y_{0} \cdot Y_{1} \cdots Y_{n}\]

where the random variables $Y_{i}$ are independent and have a uniform distribution over the interval $[0, T]$. Under which conditions is $\left\{X_{0}, X_{1}, \ldots\right\}$ (1) a martingale, (2) a submartingale, (3) a supermartingale?

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Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

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Question Posted: Apr 26, 2024 04:01 PM

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Let a discrete-time stochastic process (left{X_{0}, X_{1}, ldots ight}) be defined by [X_{n}=Y_{0} cdot Y_{1} cdots Y_{n}]

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Applied Probability And Stochastic Processes

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