What is Brownian bridge?

A Brownian bridge from $x$ to $y$ on $[t_0, t_1]$ is a Brownian motion conditioned on $W_{t_0} = x$ and $W_{t_1} = y$; from $0$ to $0$ on $[0, T]$ it can be written $W_t - (t/T)W_T$, a centred Gaussian process with covariance $s(T - t)/T$ for $s \le t$.