Taking the derivative, [itex]d[/itex], of both sides of the equation.

[operationsres]

Suppose that $B(t)$ is a Wiener process. Suppose that the following equation is true:

$B(t)(t + \frac13 B(t)) = B(t)^{0.5}$.

I've conjured this equation out of thin air (it's probably not true) to ask the following question. Does the above identity (assuming it's correct) enable us to write the following:

$dB(t)dt + \frac13 dB(t) = dB(t)^{0.5}$

?

 

[SammyS]

Suppose that $B(t)$ is a Wiener process. Suppose that the following equation is true:

$B(t)(t + \frac13 B(t)) = B(t)^{0.5}$.

I've conjured this equation out of thin air (it's probably not true) to ask the following question. Does the above identity (assuming it's correct) enable us to write the following:

$dB(t)dt + \frac13 dB(t) = dB(t)^{0.5}$

?

In a word, no.

Use the product rule.