What is the quadratic variation of ($w(t))^2$, where $w(t)$ denotes a Wiener- process and what is the expected value of it? What is $E([(w(t))^2])$?

My result is: $2(t^2)$, but knowing myself, I am not 100% sure about it.

  • $\begingroup$ $\newcommand{\E}{\Bbb{E}}$See e.g. math.stackexchange.com/questions/1028350/… for discussions about the quadratic variation of $W(t)^2$. To find $\E\left[W(t)^2\right]$, just recall that $W(t)\sim N(0,t)$ and so $\E\left[W(t)^2\right] = t$ (remember, the second moment of a $N(0,\sigma^2)$ random variable is $\sigma^2$). $\endgroup$ – Minus One-Twelfth Jun 4 at 10:30
  • $\begingroup$ Yes, it was right in my solution as well...but my question is about the expected value of the quadratic variation of Wiener- process squared...Is my result right in this case? $\endgroup$ – Kapes Mate Jun 4 at 11:02

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