Brownian Bridge Covariance
Pin a Brownian process at two endpoints and inspect the resulting covariance.
Free theory articlePin a Brownian process at two endpoints and inspect the resulting covariance.
Concept & interpretation
A Brownian bridge is a continuous-time stochastic process that is pinned at both its starting and ending points. It can be constructed by conditioning a standard Brownian motion on its value at a future time.
Experiment
Explore this process in the Brownian Bridge Covariance module.
- Set the Endpoints to "Ascending", Duration to 2.
- Set Time fraction to 0.5 and Other time fraction to 0.25.
- Observe the Covariance is exactly 0.25 and Correlation matches the calculation above.
- Change the Time fraction to 0. This moves the evaluation point exactly to the starting endpoint.
- Observe the Variance becomes 0 because the starting endpoint is pinned. The Correlation becomes "Unavailable" as division by zero variance is not defined.