 Home

Codex Wiki

Mathematics

Area of mathematics

Probability and statistics

Probability theory

Stochastic process

Brownian motion

Brownian motion with drift

For $a,b>0$,
$$
\mathbb P\!\left(\sup_{0\leq s\leq t}(W_s-as)\leq b\right)
=\Phi\!\left(\frac{b+at}{\sqrt t}\right)
-e^{-2ab}\Phi\!\left(\frac{at-b}{\sqrt t}\right).
$$
This follows from the <Brownian reflection principle> weighted by the <Cameron-Martin theorem for a linear drift>.

Finite-horizon maximum of Brownian motion with negative drift

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 29K / c / Solution

Finite-horizon maximum of Brownian motion with negative drift

 Ancestors (8)

 Incoming links (1)

 Discussion (0)

 Articles by others on the same topic (0)

Finite-horizon maximum of Brownian motion with negative drift

 Ancestors (8)

 Incoming links (1)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)