Questions / Quant research, Stochastic calculus & linear algebra
Brownian increments
W is standard Brownian motion. What is Var(W₃ − W₁)?
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Answer: 2 variance units
- W₃ − W₁ is an increment over 2 units of time.
- Its variance is 2.
Interview shortcut. Length of the interval: 3 − 1.
Takeaway. Var(W_t − W_s) = t − s.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.