In the mathematical theory of probability, Brownian meander is a continuous non-homogeneous Markov process defined as follows:
Let be a standard one-dimensional Brownian motion, and , i.e. the last time before t = 1 when visits . Then
The transition density of Brownian meander is described as follows:
For and , and writing
i.e. has the Rayleigh distribution with parameter 1, the same distribution as , where is an exponential random variable with parameter 1.