matlab开发-随机微分方程解算

% This function finds out the first two moments % of a linear Stochastic Differential Equation (LSDE) % LSDE : dy(t) = ay(t)+ b*sigma*dW(t) where W(t) is Wiener Process % Also dW(t)=n(t)dt where n(t) is Gaussian White noise % Inputs : a, b, sigma( magnitude of sqrt of PSD) and % c ( =y(0) initial conditions) % t (Time Vector) % Output :m(t)( First Moment - Mean) % M(t) (Second Moment) % Note the solution statistics shown below have been derived using Ito's % Calculus % Author: abhiruplahiri@yahoo.com function [m,M] = LSDE(a,b,sigma,c,t) m=c*exp(a*t); q=b^2*sigma^2/(2*a) p=c^2+q;; M=-q + p*exp(2*a*t); % derived using Ito's Formula %plot(t,m,t,M) %grid