EulerMaruyama.m

function [Y,Wiener] = EulerMaruyama(DriftVector,DiffusionMatrix,T,Y0,Wiener_in)

%   Purpose
%   =======
%   Find solution of the system of Ito stochastic equations with 
%   m-dimensional multi-channel noise:
%
%      / Y1 \   / f1 \        / g11  g12 ... g1m \   / dW1 \
%      | Y2 |   | f2 |        | g12  g22 ... g2m |   | dW2 |
%      | .  | = | .  | * dt + |  .      .     .  | * |  .  |
%      | .  |   | .  |        |  .         .  .  |   |  .  |
%      \ Yn /   \ fn /        \ gn1  gn2 ... gnm /   \ dWm /
%
%       Yi(t0) = Yi0, i = 1..n
%
%
%   Method
%   ======
%   Euler Maruyama method on uniform time grid:
%                                                   / I1 \   
%                                                   | I2 |
%   yi[k+1] = yi[k] + h*fi[k] + [ gi1 gi2 ... gim ] | .  |    
%                                                   | .  |
%                                                   \ Im /
%
%
%   IN
%   ==
%   1) DriftVector     - function handle that evaluates drift vector
%   2) DiffusionMatrix - function handle that evaluates matrix of 
%                        diffusion coefficients
%   3) T - vector of time points
%   4) Y0 - n-dimensional column vector with initial data
%   5) varargin - optional array of driving Wiener processes 
%                 (same as in the output below)
%
%
%   OUT
%   ===
%   Y - K-by-n solution array. Each row in Y corresponds to the solution 
%       at a time returned in the corresponding row of T
%   Wiener - M-by-K-dimensional array of the driving Wiener processes. 


    % number of equations
    N = max(length(Y0));
    
    % dimension of the noise
    M = size(DiffusionMatrix(1,Y0),2);
    
    % number of points in time discretization
    K = max(length(T));

    % step size
    dt = T(2) - T(1);

    % initialize solution array
    Y = zeros(N,K);
    
    Y(:,1) = Y0(:);
    
    
    % generate array of driving Wiener processes
    if ( nargin == 4 )
        Wiener = BrownianMotion(dt,K,M);
    else 
        Wiener = Wiener_in;
    end
    
    % loop in time
    for i = 2:K        
        % generate vector of noise increments
        dW = Wiener(:,i) - Wiener(:,i-1);

        F = DriftVector(T(i),Y(:,i-1));
        G = DiffusionMatrix(T(i),Y(:,i-1));
                
        % update solution
        Y(:,i) = Y(:,i-1) + F * dt + G * dW;
    end
   
end