2. Stochastic Processes

Brownian Motion — Quiz

Test your understanding of brownian motion with 5 practice questions.

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Practice Questions

Question 1

Which function describes the covariance of a standard Brownian motion $B(t)$?

Question 2

For a standard Brownian motion $B(t)$, what is $P\bigl(|B(4)|>2\bigr)$?

Question 3

The quadratic variation of a standard Brownian motion $B(t)$ over $[0,T]$ is $\lim_{\lVert PVert\to0}\sum (B(t_i)-B(t_{i-1}))^2$. Almost surely, this limit equals:

Question 4

Which of the following processes is a martingale with respect to the natural filtration of $B(t)$?

Question 5

Which of the following describes the scaling property of Brownian motion?