represents the Brownian bridge process from value a at time t1 to value b at time t2 with volatility σ.
represents the standard Brownian bridge process from value a at time t1 to value b at time t2.
represents the standard Brownian bridge process pinned at 0 at times t1 and t2.
represents the standard Brownian bridge process pinned at 0 at time 0 and at time 1.
- BrownianBridgeProcess is also known as pinned Brownian motion process.
- BrownianBridgeProcess is a continuous-time and continuous-state random process.
- The state for a Brownian bridge process satisfies and .
- The state follows NormalDistribution[a+(b-a) (t-t1)/(t2-t1),].
- The parameters σ, t1, t2, a, and b can be any real numbers, with σ positive and t2 greater than t1.
- BrownianBridgeProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examplesopen allclose all
Basic Examples (3)
Basic Uses (8)
Process Slice Properties (5)
CentralMoment and its generating function:
FactorialMoment has no closed form for symbolic order:
Cumulant and its generating function:
Properties & Relations (9)
A Brownian bridge process is a special ItoProcess:
As well as StratonovichProcess:
A Brownian bridge process initially follows its corresponding WienerProcess:
The distribution of the absolute supremum of a BrownianBridgeProcess follows a Kolmogorov distribution:
Compare to the corresponding BrownianBridgeProcess:
A Brownian bridge is a conditioned WienerProcess: