RR_example.org

Generate data

std::default_random_engine generator;
std::normal_distribution<double> distribution(0.0,1.0);

int N=10;
double dt = 0.1;
double mean = 0.0;
double diffusion = 0.5;

std::vector<double> timepoints(N);
std::vector<double> values(N);

double t, x, dw;
for(int i = 0;i<N;i++){
  t = i*dt;
  dw = distribution(generator);
  x = x + (mean-x)*dt + sqrt(2.*diffusion)*dw;

  std::cout << t << " " << x << std::endl;
}

#+RESULTS[2908baa678d31e0ace01e9a0fc9b49c65facbb19]: initial_data

0	-0.121966
0.1	-1.19659
0.2	-0.392639
0.3	-1.42856
0.4	-1.25244
0.5	-0.382359
0.6	-0.310517
0.7	-0.806102
0.8	-0.26296
0.9	-0.0359645

Analyse the data

timeseries = np.array(timeseries)
print(f"The mean is {np.mean(timeseries[:,1])}")

The mean is -0.61900975

We note that the value of the mean is src_python[:var timeseries=initial_data]{import numpy as np; timeseries = np.array(timeseries); return np.mean(timeseries[:,1])} {{{results(-0.61900975)}}} whi is consistent with the true value (0) because the length of the timeseries is only src_python[:var timeseries=initial_data]{import numpy as np; return len(timeseries)} {{{results(10)}}}.

values = np.array(x)[:,1]
return np.mean(values)

Another paragraph about the mean, whose value is call_mean(initial_data) {{{results(-0.61900975)}}}.

Plotting

import matplotlib.pyplot as plt
timeseries = np.array(timeseries)
plt.plot(timeseries[:,0], timeseries[:,1])
plt.savefig("myfig.png")