Scaled Random Walk Approximation to BM
Purpose
Step function approximation to weiner
> library(sde)
> par(mfrow = c(2, 2))
> T <- 100
> t <- 1/100
> main <- paste(" N =", T)
> x <- seq(0, 1, t)
> y <- c(0, (cumsum(rnorm(T)/sqrt(T))))
> plot(x, y, type = "s", main = main)
> T <- 1000
> t <- 1/T
> main <- paste(" N =", T)
> x <- seq(0, 1, t)
> y <- c(0, (cumsum(rnorm(T)/sqrt(T))))
> plot(x, y, type = "s", main = main)
> T <- 10000
> t <- 1/T
> main <- paste(" N =", T)
> x <- seq(0, 1, t)
> y <- c(0, (cumsum(rnorm(T)/sqrt(T))))
> plot(x, y, type = "s", , main = main)
> x <- BM(N = T)
> main <- "BM"
> plot.ts(x, , main = main) |
