New answers tagged itos-lemma
2
For Itô Processes $dX(t) = \mu(t) \mathrm{d}t + \sigma(t) \mathrm{d}W(t)$ you have the result that (under appropriate assumptions which ensure that the local martingale is a martingale, e.g. $E( (\int \sigma(t)^2 \mathrm{d}t )^{1/2} ) < \infty$, etc.): $X$ is a martingale $\Leftrightarrow$ $\mu(t) = 0$.
So in order to check if a process $X$ is a ...
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Rather simply and generally when you take the stochastic differential of a process and get no drift term but simply an ito integral, then this process is a martingale.
From memory that's how you retrieve some pde equations whose solutions lead to martingale (take the differential, look at the dt partial differentials term, then look for solution that would ...
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