# What is Variance of delta of brownian motion [closed]

I am new to this.

If variance of Brownian motion b is t, what is the variance of db?

db is delta of b

Let $$(B_t)$$ be a standard Brownian motion. Then, $$B_t\sim N(0,t)$$ and $$B_t-B_s\sim N(0,t-s)$$.
Informally, you can say $$\mathrm{d}B_t\sim N(0,\mathrm{d}t)$$ where $$\mathrm{d}B_t=B_{t+\mathrm{d}t}-B_t$$ is an infinitesimal increment.
• @InfoLearner good question. A constant can be pulled out of the variance if you remember to square it, i.e. $\sigma \mathrm{d}B_t\sim N(0,\sigma^2\mathrm{d}t)$. – KeSchn Jan 19 at 10:46