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BUILT-IN MATHEMATICA SYMBOL
BrownianBridgeProcess
BrownianBridgeProcess[
, {t1, a}, {t2, b}]
represents the Brownian bridge process from value a at time 
to value b at time 
with volatility .
BrownianBridgeProcess[{t1, a}, {t2, b}]
represents the standard Brownian bridge process from value a at time 
to value b at time 
.
BrownianBridgeProcess[t1, t2]
represents the standard Brownian bridge process pinned at 
at times 
and 
.
BrownianBridgeProcess[]
represents the standard Brownian bridge process pinned at 
at time 
and at time 
.
Details
- BrownianBridgeProcess is also known as pinned Brownian motion.
- 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 ,
, 
, a, and b can be any real numbers, with positive and 
greater than 
. - BrownianBridgeProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
New in 9
