Simulate a Brownian bridge process pinned at 0 at both ends:

Mean and variance functions:

Covariance function:

Useful shortcuts evaluate to their full form counterparts:

A Brownian bridge is not weakly stationary:

A Brownian bridge process does not have independent increments:

Compare to the product of expectations:

Conditional cumulative probability distribution:

A Brownian bridge process is a special ItoProcess:

As well as StratonovichProcess:

A Brownian bridge process is a solution to the stochastic differential equation :

Compare with the corresponding smooth solution:

A Brownian bridge process initially follows its corresponding WienerProcess:

The distribution of the absolute supremum of a BrownianBridgeProcess follows a Kolmogorov distribution:

Simulate sample distribution:

Compare the cumulative histogram with the cumulative distribution function of a Kolmogorov distribution:

BrownianBridgeProcess can be simulated directly from WienerProcess:

Apply a transformation to the random sample:

Compare to the corresponding BrownianBridgeProcess:

A Brownian bridge is a conditioned WienerProcess:

Compare to the CDF of the slice distribution of a Brownian bridge:

Simulation is supported only within the process support:

Simulate from 0 to 1:

Simulate on a part of the support:

Simulate a Brownian bridge process in two dimensions:

Simulate a Brownian bridge process in three dimensions:

Simulate 500 paths from a Brownian bridge process:

Take a slice at 1/2 and visualize its distribution:

Plot paths and histogram distribution of the slice distribution at 1/2: