A Brownian bridge is a continuous-time stochastic process B(t) whose probability distribution is the conditional probability distribution of a Wiener process W(t) (a mathematical model of Brownian motion) given the condition that B(1) = 0. More precisely:
The expected value of the bridge is zero, with variance t(1 − t), implying that the most uncertainty is in the middle of the bridge, with zero uncertainty at the nodes. The covariance of B(s) and B(t) is s(1 − t) if s < t. The increments in a Brownian bridge are not independent.
Read more about Brownian Bridge: Relation To Other Stochastic Processes, Intuitive Remarks, General Case
Famous quotes containing the word bridge:
“Oh, who will now be able to relate how Pantagruel behaved in face of these three hundred giants! Oh my muse, my Calliope, my Thalie, inspire me now, restore my spirits, because here is the ass’s bridge of logic, here is the pitfall, here is the difficulty of being able to describe the horrible battle undertaken.”
—François Rabelais (1494–1553)