- #1

WMDhamnekar

MHB

- 376

- 28

Consider the sequence $\{X_n\}_{n\geq 1}$ of independent random variables with law $N(0,\sigma^2)$. Define the sequence $Y_n= exp\bigg(a\sum_{i=1}^n X_i-n\sigma^2\bigg),n\geq 1$ for $a$ a real parameter and $Y_0=1.$

Now how to find the values of $a$ such that $\{Y_n\}_{n\geq 1}$ is martingale, submartingale, supermartigale?Solution:I have no idea to answer this question. I searched on internet, but i didn't get any clew about the way using which one can answer this question till now. If any member knows the correct answer, he may reply with correct answer.

Now how to find the values of $a$ such that $\{Y_n\}_{n\geq 1}$ is martingale, submartingale, supermartigale?Solution:I have no idea to answer this question. I searched on internet, but i didn't get any clew about the way using which one can answer this question till now. If any member knows the correct answer, he may reply with correct answer.

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