Determine dynamics of stochastic differential equations (SDE)

[AxeO]

Hi guys, I´ve just started with SDE and Itô´s lemma but don't really know where and how to begin. I´ve realized that both a Reimann integral and Itô integral is needed both cannot figure out how to solve these questions. Would be much appreciated if someone would help me.

View attachment 3526

 

[Siron]

What exactly do you mean by 'determine the dynamics of'?

An elementary version of Ito's formula states that for $f \in C^2(\mathbb{R})$ and a semimartingale $X$, we have
$$f(X_t) =f(X_0) + \int_{0}^{t} f'(X_s)dX_s+\frac{1}{2}\int_{0}^{t}f''(X_s)d\langle X_s, X_s \rangle$$

So, can you be more clear about your troubles with this exercice?

 

[AxeO]

Sorry for being unclear, but what i meant was how to determine the diffusion of dV_t of the different functions. But I made an Taylor expansion and let \DeltaX and \Deltat be infinite small which gave me some multiplication rules which i could use to solve it (Itôs lemma). So I´ve already solved this question, thanks anyways for the help.