# BrownianBridgeProcess

BrownianBridgeProcess[σ,{t1,a},{t2,b}]

represents the Brownian bridge process from value a at time t1 to value b at time t2 with volatility σ.

BrownianBridgeProcess[{t1,a},{t2,b}]

represents the standard Brownian bridge process from value a at time t1 to value b at time t2.

BrownianBridgeProcess[t1,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.

# Details • 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.

# Examples

open all close all

## Basic Examples(3)

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

 In:= Out= In:= Out= Mean and variance functions:

 In:= Out= In:= Out= Covariance function:

 In:= Out= In:= Out= ## Neat Examples(3)

Introduced in 2012
(9.0)