max_Bessel_bridge_path_sampler: Bessel Bridge path sampler given maximum

In rchan26/layeredBB: Simulates layered Brownian bridges using C++ and Rcpp

Bessel Bridge path sampler given maximum

Description

Simulation of a path of a Bessel bridge at given times, given maximum occurs at time tuu

Usage

max_Bessel_bridge_path_sampler(x, y, s, t, m, tau, times, checks = TRUE)

Arguments

x	start value of Bessel bridge
y	end value of Bessel bridge
s	start time of Bessel bridge
t	end time of Bessel bridge
m	maximum point
tau	time of maximum point
times	vector of real numbers to simulate Bessel bridge
checks	logical value to determine if arguments that are passed into the function are checked. Things that are checked include that s < t, that requested simulation times are in [s,t], that m >= max(x,y) and that if tau == s or tau == t, then m == x or m == y, respectivelys

Value

A list with the following components

full_path

Matrix of the simulated Bessel bridge path at all included time points, i.e. s, t and times. The times are sorted and duplicates are removed. The first row are the points of the Brownian bridge (named 'X') second row are corresponding times (named 'time')

simulated_path

Matrix of the simulated Bessel bridge path only at the specified times passed into the function, i.e. the times vector. The times are not sorted and duplicates are not removed. The first row are the points of the Bessel bridge (named 'X') second row are corresponding times (named 'time')

remove_m_path

Matrix of the simulated Bessel bridge path only at all included times points excluding tau. These times are sorted and duplicates are removed. The first row are the points of the Bessel bridge (named 'X') second row are corresponding times (named 'time'). Note that the maximum point is included if it is passed into the times vector

Examples

# simulating a path at times = c(0.2, 0.4, 0.8) for a Bessel bridge starting 
# at 0 and ending at 0 in time [0,1] given maximum is at 0.4 at time 0.6
max_Bessel_bridge_path_sampler(x = 0,
                               y = 0,
                               s = 0,
                               t = 1,
                               m = 0.4,
                               tau = 0.6,
                               times = c(0.2, 0.4, 0.8))

# note that remove_m_path will still include the minimum if passed into times
# also note that simulated_path does not remove duplicates passed into times
max_Bessel_bridge_path_sampler(x = 0,
                               y = 0,
                               s = 0,
                               t = 1,
                               m = 0.4,
                               tau = 0.6,
                               times = c(0.2, 0.4, 0.6, 0.8, 0.6))

# another example
start <- runif(1, -1, 1)
end <- runif(1, -1, 1)
max <- max_sampler(x = start,
                   y = end,
                   s = 0,
                   t = 1,
                   low_bound = max(start, end)+0.2,
                   up_bound = max(start, end)+0.4)
path <- max_Bessel_bridge_path_sampler(x = start,
                                       y = end,
                                       s = 0,
                                       t = 1,
                                       m = max['max'],
                                       tau = max['tau'],
                                       times = seq(0, 1, 0.01))$full_path
plot(x = path['time',], y = path['X',], pch = 20, xlab = 'Time', ylab = 'X')
lines(x = path['time',], y = path['X',])
points(x = max['tau'], y = max['max'], col = 'red', pch = 20)

rchan26/layeredBB documentation built on March 25, 2022, 3:44 a.m.