IFSM | R Documentation |
IFSM operator
IFSM(x, cf, a, s, k = 2)
x |
where to approximate the function |
cf |
the vector of coefficients phi_i |
s |
the vector of coefficients s_i in: w_i = s_i *x + a_i |
a |
the vector of coefficients a_i in: w_i = s_i *x + a_i |
k |
number of iterations, default = 2 |
This operator is intended to approximate a function on L2[0,1]. If āuā is simulated, then the IFSM can be used to simulate a IFSM version of āuā.
The value of the approximate target function.
S. M. Iacus
Iacus, S.M, La Torre, D. (2005) IFSM representation of Brownian motion with applications to simulation, forthcoming.
require(ifs) set.seed(123) n <- 50 dt <- 1/n t <- (1:n)*dt Z <- rnorm(n) B <- sqrt(dt)*cumsum(Z) ifsm.w.maps() -> maps a <- maps$a s <- maps$s ifsm.setQF(B, s, a) -> QF ifsm.cf(QF$Q,QF$b,QF$L1,QF$L2,s)-> SOL psi <- SOL$psi t1 <- seq(0,1,length=250) as.numeric(sapply(t1, function(x) IFSM(x,psi,a,s,k=5))) -> B.ifsm old.mar <- par()$mar old.mfrow <- par()$mfrow par(mfrow=c(2,1)) par(mar=c(4,4,1,1)) plot(t1,B.ifsm,type="l",xlab="time",ylab="IFSM") plot(t,B,col="red",type="l",xlab="time",ylab="Euler scheme") par(mar=old.mar) par(mfrow=old.mfrow)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.