AppliedMultiple choice
Hitting a barrier · Part 2 of 4
is a standard Brownian motion started at 0, with no drift. The parts ask about the first time it reaches given levels.
With no time limit and no other barrier, what is the expected time for the path to first reach +1?
- A1, from a² with a = 1
- BInfinite, although the level is reached with probability one
- C2, twice the variance of W₁
- DUndefined, because the path may never reach +1 at all without a drift
The worked solution is in Premium
The answer, the full working and the one idea to take away – for this and all 1,322 questions in the bank. Answer it in practice and your working is marked, with a known mistake named when you make one.
Learn the method
Hitting times, the reflection principle and the running maximum
More stochastic calculus questions
- A Brownian motion with drift 0.5 per unit time starts at zero.Applied
- Standard Brownian motion starts at 0. What is the probability it hits +1 before −2?Applied
- Standard Brownian motion starts at 0 and stops on hitting +1 or −2.Applied
- For a standard Brownian motion, what is Pr(max _(t ≤ 4)Wₜ ≥ 2), to four decimal places?Advanced
- Xₜ = 0.5t+Wₜ starts at 0. What is the probability it hits +1 before −1, to three decimals?Advanced
- A driftless Brownian motion starts at 0.Advanced