Simulating Brownian motion in R. Is this correct?

I have a Weiner process ${W(t)}_{tge0}$ with $sigma^2=text{Var}(W(1))=1$. For a real constant $epsilon>0$ consider the differential ratio process $Delta_epsilon={Delta_epsilon(t)}_{r>0}$ given by
begin{equation}
Delta_epsilon(t) = frac{W(t+epsilon)-W(t)}{epsilon}, quad text{for} t>0.
end{equation}

I want to simulate a sample path of ${Delta_epsilon(t)}_{tin(0,1]}$ for small $epsilon>0$ in Rstudio.

Simulating a basic Weinerprocess/Brownian motion is easy in R, one can do it by the function rweiner() or by plotting the cumulative sum of standard normally distributed variables. The part that confuses me is how to simulate the $W(t+epsilon)$. What I’ve done is used rwiener() and simply passed the end parameter to $1+epsilon$.

epsilon = 10e-1
weinerEps = rwiener(end = 1+epsilon, frequency = 1000)
weiner = rwiener(end = 1, frequency = 1000)

Delta = (wienerEps - wiener)/epsilon

plot(Delta , type="l")

I’m not sure this is correct though.

library('e1071')
epsilon = 1e-1  # 1/10=1e-1 and not 10e-1=1.
freq    = 1000
wiener  = rwiener(end = 1+epsilon, frequency = freq)
w       = wiener[1:1000];
w_eps   = wiener[(1+freq*epsilon):(1000+freq*epsilon)];
Delta   = (w_eps - w)/epsilon
plot(Delta , type="l")