In AnthonyTedde/RandomProcesses: Random Processes

The purpose of this paper is to show that the distribution of the scaled random walk goes to the one of the normal law as the time intervals go to zero.

Random walk generation

timeT <- 4
anonymous <- function(n){
  RandomWalk::trwalkGenerator(time_to_maturity = timeT,
                scale = n, 
                full = T)[[n * timeT + 1]]
}
rws <- lapply(1:100, anonymous)

interval <- (rws[[100]]$Mt[1] - rws[[100]]$Mt[length(rws[[100]]$Mt)]) / 
  (length(rws[[100]]$Mt) - 1)

ggplot2::ggplot(rws[[100]], ggplot2::aes(Mt)) +
  ggplot2::geom_histogram(ggplot2::aes(weight = Pr / interval), binwidth = interval) +
  ggplot2::scale_x_continuous(limits = c(-7.5, 7.5)) + 
  ggplot2::stat_function(fun = dnorm,
                         color = "blue",
                         args = list(mean = 0, 
                                     sd = sqrt(timeT)))

AnthonyTedde/RandomProcesses documentation built on Dec. 14, 2021, 10:39 a.m.