# Tag Info

### Are differentials on their own in stochastic calculus just an abuse of notation?

Differentials in stochastic calculus have very precise interpretations. The stochastic differential equation in differential form $$dX_t = \mu (t, X_t) dt + \sigma (t, X_t) dB_t$$ translates precisely ...
• 12.9k
Accepted

• 146
1 vote

### Using Ito's Lemma to take a stochastic integral

Please avoid to ask too many questions at the same time in future posts. Let's tackle the side questions first. First side question. I mean, why not ? If you have a stochastic variable $X_t$ itself ...
• 8,328
1 vote
Accepted

The trick to being able to use the Optional Stopping Theorem here is to realize that, in the equation $\alpha (\alpha - 1) = 2\lambda$, we can always choose $\alpha < 0$. This implies $Y_t = (B_{t ... • 13.5k 1 vote ### Verifying Ito isometry for simple stochastic processes A simple process$\Phi = (\Phi_t)_{t\geq 0}\in\mathcal{E}$is a process of the form $$\Phi_t = \sum_{i=0}^{n-1}U_i1_{(t_i,t_{i+1}]}(t)$$ where$0=t_0<\dots<t_n<\infty$and$U_i\in b\mathcal{F}...

Only top scored, non community-wiki answers of a minimum length are eligible