added convergence test main poisson

experiments/tests_period_7/local_main_poisson.jl

@@ -8,6 +8,7 @@ function Y(t, sig, A::Function, f::Function, y0)
 end
 
 using Plots
+using Statistics
 sig = 1.0
 A(s) = s
 f(s) = -s^3 + 2 * s
@@ -16,6 +17,22 @@ t = 1.0
 sol(s) = s^2
 errors = []
 nsim1 = 10^3
+
+sigs = exp10.(range(log10(1.0), log10(10000.0), length=10))
+stds = []
+for sig in sigs
+ push!(stds, mean((Y(t, sig, A, f, q) - sol(t))^2 for _ in 1:nsim1))
+end
+
+plot(sigs, stds, st=:scatter, xscale=:log10, yscale=:log10, label="std")
+ylabel!("std")
+xlabel!("sig")
+c = 1.5
+plot!(sigs, c * sigs .^ -0.5, label="sig^-1.5")
+plot!(sigs, c * sigs .^ -1, label="sig^-1.5")
+plot!(sigs, c * sigs .^ -1.5, label="sig^-1.5")
+
+
 for _ in 1:1000
  e = sum(Y(t, 1, A, f, q) for _ in 1:nsim1) / nsim1 - sol(t)
  push!(errors, e)

latex/main paper/main.tex

@@ -1632,8 +1632,8 @@ \subsection{First Passage Sampling}
  and \cite{ji_reusing_2012}.
 \end{related}
 
-Path stitching combined with resampling paths for applied to the semi-discretized heat equation can be
-interpreted as estimation with a U-statistic. The recursive path is a stitching of scaled i.i.d. subpaths.
+% Path stitching combined with resampling paths for applied to the semi-discretized heat equation can be
+% interpreted as estimation with a U-statistic. The recursive path is a stitching of scaled i.i.d. subpaths.
 
 
 \section{Limitations and Future Work}