Find a regular process $A_t$, such that


is a martingale. $B_t$ is Brownian motion.

I'm totally lost. I have an idea that I should apply Ito formula here, but I don't know where to start...

  • 3
    $\begingroup$ Apply Itô's formula to $t B_t^2$ $\endgroup$
    – saz
    Feb 9, 2020 at 19:04

1 Answer 1


I will post the solution using the suggestion by saz here for those who are interested.

Applying Ito formula to function $F(x,t)=tx^2$ we get


It can be proven that integral $\int_0^tsB_sdB_s$ is a martingale. Since $A_t$ is a regular process, we get:



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