MHB Determine dynamics of stochastic differential equations (SDE)

AI Thread Summary
The discussion revolves around understanding stochastic differential equations (SDE) and Itô's lemma. The initial poster seeks guidance on determining the dynamics of SDEs, specifically how to apply Itô's formula and the necessary integrals. They clarify their confusion regarding the diffusion process and mention using Taylor expansion to derive multiplication rules for solving their questions. Ultimately, they express gratitude for the assistance after resolving their query. The conversation highlights the importance of Itô's lemma in analyzing the behavior of stochastic processes.
AxeO
Messages
2
Reaction score
0
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
 

Attachments

Physics news on Phys.org
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?
 
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.
 
Back
Top