rBB {smam}

Sampling from a Brownian bridge path give a grid time

Description

A Brownian bridge is a continuous-time stochastic process B(t) whose probability distribution is the conditional probability distribution of a standard Wiener process W(t) subject to the condition (when standardized) that W(T) = 0, so that the process is pinned to the same value at both t = 0 and t = T. The implementation here is a generalized Brownian bridge that allows start point and end point at different locations.

Usage

rBB(time, start_pt, end_pt, sigma)

Arguments

time

time points at which observations are to be simulated

start_pt

the start point location of Brownian bridge

end_pt

the end point location of Brownian brige

sigma

volatility parameter of the Brownian motion

Value

A data.frame whose first column is the time points and second column is coordinate of the locations.

Examples

## Brownian bridge starting from location 0 and ending at location 1
## with sigma 0.1 from time 0 to time 10
plot(rBB(seq(0, 10, length.out = 100), 0, 1, 0.1), type = "l")