fix length n |-> n+1

docs/literate/examples/01-wiener_linearhomogeneous.jl

@@ -165,7 +165,7 @@ info = (
 
 # The *target* solution as described above is implemented as
 
-function target_solver!(xt::Vector{T}, t0::T, tf::T, x0::T, f::F, yt::Vector{T}, rng::AbstractRNG) where {T, F}
+target_solver! = function (xt::Vector{T}, t0::T, tf::T, x0::T, f::F, yt::Vector{T}, rng::AbstractRNG) where {T, F}
     axes(xt) == axes(yt) || throw(
         DimensionMismatch("The vectors `xt` and `yt` must match indices")
     )

docs/literate/examples/10-risk.jl

@@ -211,7 +211,7 @@ nothing # hide
 
 # The actual surplus is $U_t = X_t - O_t - C_t$, so we may visualize a sample solution of the surplus by subtracting these two noises from the solution of the above RODE.
 
-plt_surplus = plot(range(t0, tf, length=ntgt), suite.xt .- suite.yt[:, 1] .- suite.yt[:, 3], xaxis="\$t\$", yaxis="\$u\$", label="\$U_t\$", linecolor=1)
+plt_surplus = plot(range(t0, tf, length=ntgt+1), suite.xt .- suite.yt[:, 1] .- suite.yt[:, 3], xaxis="\$t\$", yaxis="\$u\$", label="\$U_t\$", linecolor=1)
 
 #
 

docs/src/examples/01-wiener_linearhomogeneous.md

@@ -186,7 +186,7 @@ info = (
 The *target* solution as described above is implemented as
 
 ````@example 01-wiener_linearhomogeneous
-function target_solver!(xt::Vector{T}, t0::T, tf::T, x0::T, f::F, yt::Vector{T}, rng::AbstractRNG) where {T, F}
+target_solver! = function (xt::Vector{T}, t0::T, tf::T, x0::T, f::F, yt::Vector{T}, rng::AbstractRNG) where {T, F}
     axes(xt) == axes(yt) || throw(
         DimensionMismatch("The vectors `xt` and `yt` must match indices")
     )

docs/src/examples/10-risk.md

@@ -247,7 +247,7 @@ nothing # hide
 The actual surplus is $U_t = X_t - O_t - C_t$, so we may visualize a sample solution of the surplus by subtracting these two noises from the solution of the above RODE.
 
 ````@example 10-risk
-plt_surplus = plot(range(t0, tf, length=ntgt), suite.xt .- suite.yt[:, 1] .- suite.yt[:, 3], xaxis="\$t\$", yaxis="\$u\$", label="\$U_t\$", linecolor=1)
+plt_surplus = plot(range(t0, tf, length=ntgt+1), suite.xt .- suite.yt[:, 1] .- suite.yt[:, 3], xaxis="\$t\$", yaxis="\$u\$", label="\$U_t\$", linecolor=1)
 ````
 
 ````@example 10-risk

docs/src/noises/colored.md

@@ -53,8 +53,8 @@ y0 = 0.0
 t0 = 0.0
 tf = 2.0
 n = 2^10
-tt = range(t0, tf, length=n)
-dt = (tf - t0) / (n - 1)
+tt = range(t0, tf, length=n+1)
+dt = (tf - t0) / n
 nothing # hide
 ```
 
@@ -72,7 +72,7 @@ ou_noises = (OrnsteinUhlenbeckProcess(t0, tf, y0, 1/τ, √(2/τ)) for τ in τs
 nothing # hide
 ```
 
-This `noises` is a `Tuple` where each element is an OU sampler. With each sampler `noises[i]`, we draw a sample path with `rand!(rng, noises[i], yt)`, with a given random number generator `rng` and a vector of floats `yt` of size `n`, so that this sampling fills up the pre-allocated vector `yt` with a sample path over the interval `t0` to `tf`, with the corresponding resolution `dt = (tf - t0) / (n - 1)`. For that, we set up the `rng`, used for reproducibility.
+This `noises` is a `Tuple` where each element is an OU sampler. With each sampler `noises[i]`, we draw a sample path with `rand!(rng, noises[i], yt)`, with a given random number generator `rng` and a vector of floats `yt` of size `n+1`, so that this sampling fills up the pre-allocated vector `yt` with a sample path over the interval `t0` to `tf`, with the corresponding resolution `dt = (tf - t0) / n`. For that, we set up the `rng`, used for reproducibility.
 
 ```@example colored
 rng = Xoshiro(123)
@@ -81,8 +81,8 @@ rng = Xoshiro(123)
 Let us visualize a sample path of these process. We define the resolution, pre-allocate some vectors, and compute the sample paths.
 
 ```@example colored
-w_t = Vector{Float64}(undef, n) # for the white noise
-ous_t = [Vector{Float64}(undef, n) for τ in τs] # for the OU noises
+w_t = Vector{Float64}(undef, n+1) # for the white noise
+ous_t = [Vector{Float64}(undef, n+1) for τ in τs] # for the OU noises
 nothing # hide
 ```
 

docs/src/noises/fBm.md

@@ -28,7 +28,7 @@ y0 = 0.0
 t0 = 0.0
 tf = 2.0
 n = 2^9
-tt = range(t0, tf, length=n)
+tt = range(t0, tf, length=n+1)
 nothing # hide
 ```
 
@@ -50,7 +50,7 @@ This `noise` is a `Dict` with the keys being the chosen Hurst parameters and wit
 
 ```@example fBm
 rng = Xoshiro(123)
-yt = Vector{Float64}(undef, n)
+yt = Vector{Float64}(undef, n+1)
 nothing # hide
 ```
 
@@ -109,7 +109,7 @@ nothing # hide
 Now we generate the sets of sample paths for each Hurst parameter.
 
 ```@example fBm
-W = Dict(H => Matrix{Float64}(undef, n, m) for H in Hs)
+W = Dict(H => Matrix{Float64}(undef, n+1, m) for H in Hs)
 for H in Hs
     for i in 1:m
         rand!(rng, noise[H], view(W[H], :, i))

docs/src/noises/homlin.md

@@ -90,8 +90,8 @@ We start by setting the time interval, the mesh parameters, and the number of sa
 t0 = 0.0
 tf = 2.0
 n = 2^10
-tt = range(t0, tf, length=n)
-dt = (tf - t0) / (n - 1)
+tt = range(t0, tf, length=n+1)
+dt = (tf - t0) / n
 m = 200
 nothing # hide
 ```
@@ -118,8 +118,8 @@ For comparison, we generate a bunch of sample paths with both constructors and c
 ```@example homlin
 rng = Xoshiro(123)
 
-gBmt = Matrix{Float64}(undef, n, m)
-Yt = Matrix{Float64}(undef, n, m)
+gBmt = Matrix{Float64}(undef, n+1, m)
+Yt = Matrix{Float64}(undef, n+1, m)
 
 for j in 1:m
     rand!(rng, noise, view(gBmt, :, j))