Sim.DiffProc (version 2.5)

BBF: Creating Flow of Brownian Bridge Model

Description

Simulation flow of brownian bridge model.

Usage

BBF(N, M, t0, T, x0, y, output = FALSE)

Arguments

N

size of process.

M

number of trajectories.

t0

initial time.

T

final time.

x0

initial value of the process at time t0.

y

terminal value of the process at time T.

output

if output = TRUE write a output to an Excel (.csv).

Value

• data.frame(time,x) and plot of process.

Details

The function BBF returns a flow of the brownian bridge starting at x0 at time t0 and ending at y at time T. It is defined as : $$Xt(t0,x0,T,y) = x0 + W(t-t0) - (t-t0/T-t0)*(W(T-t0)-y+x0)$$ This process is easily simulated using the simulated trajectory of the Wiener process W(t).

See Also

BB simulation brownian bridge Model, diffBridge Diffusion Bridge Models, BMN simulation brownian motion by the Normal Distribution , BMRW simulation brownian motion by a Random Walk, GBM simulation geometric brownian motion, ABM simulation arithmetic brownian motion, snssde Simulation Numerical Solution of SDE.

Examples

## flow of brownian bridge model
## starting at x0 =1 at time t0=0 and ending at y = -2 at time T =1.
BBF(N=1000,M=5,t0=0,T=1,x0=-1,y=2)