function n = OU_process(simulLen, Dt, tau, sigma_2, seed)
%OU_PROCESS Exact numerical solution of the OrnsteinUhlenbeck (OU) process
% modified by Stefano Cavallari from the original code of Daniel Charlebois
%
% n = OU_process(simulLen, Dt, tau, sigma_2, seed),
% where
% simulLen = number of samples of the OU process in output
% Dt = time step of the OU process in output. Units of (ms)
% tau = relaxation time of the OU process, see eq. 2 of Cavallari et al
% 2014. Units of (ms)
% note that Dt and tau must have the same units of time (not necessarily ms)
% sigma_2 = it is the variance(i.e. sigma^2) of the OU process in output
% (see eq. 2 of Cavallari et al 2014). The units of sigma^2 set the units
% of the OU process in output. Units of [(spikes/ms)/Dt]
% seed = seed for the random number generator (integer number)
%
% The OU process equation can be written as (Gillespie 1996):
% dn/dt = n/tau + sqrt(c) * eta(t)
% and the parameter c (diffusion constant) corresponds to (2*sigma^2/tau)
% with sigma e tau defined as in the eq. 2 of Cavallari et al 2014
c=2*sigma_2/tau;
n=zeros(simulLen,1);
randn('state',seed);
n(1) = 0;
for i=2:simulLen
r1 = randn;
n(i) = n(i1)*exp(Dt/tau) + sqrt((c*tau*0.5)*(1(exp(Dt/tau))^2))*r1;
end
