# Simulation the event times occuring in (0,T) of the delayed renewal process
# with stationary increments such that T2 ~ U(0,1)
T <- 100
t <- 0
I <- 0
# The jump times of the renewal process are stored in S
S <- c()
repeat{
u <- runif(1)
# The distribution of T1 is given by 1 - sqrt(1 - T2)
if(I == 0){
u <- 1 - sqrt(1 - u)
}
# A new interarrival time is added to time t
t <- t + u
if(t > T){
break
}
I <- I + 1;
S <- cbind(S,t)
}
# Plot
plot(c(0,S), seq(0, length(S), 1), type="s", xlab='t', ylab='N_t')