View difference between Paste ID: Khp3T952 and EasayNG2

-%EM Euler-Maruyama method on linear SDE
+%EM Euler-Maruyama method on linear SDE
-%
+%
-% SDE is dX = lambda*X dt + mu*X dW, X(0) = Xzero,
+% SDE is dX = lambda*X dt + mu*X dW, X(0) = Xzero,
-% where lambda = 2, mu = 1 and Xzero = 1.
+% where lambda = 2, mu = 1 and Xzero = 1.
-%
+%
-% Discretized Brownian path over [0,1] has dt = 2^(-8).
+% Discretized Brownian path over [0,1] has dt = 2^(-8).
-% Euler-Maruyama uses timestep R*dt.
+% Euler-Maruyama uses timestep R*dt.
-randn(’state’,100)
+randn(’state’,100)
-lambda = 2; mu = 1; Xzero = 1; % problem parameters
+lambda = 2; mu = 1; Xzero = 1; % problem parameters
-T = 1; N = 2^8; dt = 1/N;
+T = 1; N = 2^8; dt = 1/N;
-dW = sqrt(dt)*randn(1,N); % Brownian increments
+dW = sqrt(dt)*randn(1,N); % Brownian increments
-W = cumsum(dW); % discretized Brownian path
+W = cumsum(dW); % discretized Brownian path
-Xtrue = Xzero*exp((lambda-0.5*mu^2)*([dt:dt:T])+mu*W);
+Xtrue = Xzero*exp((lambda-0.5*mu^2)*([dt:dt:T])+mu*W);
-plot([0:dt:T],[Xzero,Xtrue],’m-’), hold on
+plot([0:dt:T],[Xzero,Xtrue],’m-’), hold on
-R = 4; Dt = R*dt; L = N/R; % L EM steps of size Dt = R*dt
+R = 4; Dt = R*dt; L = N/R; % L EM steps of size Dt = R*dt
-Xem = zeros(1,L); % preallocate for efficiency
+Xem = zeros(1,L); % preallocate for efficiency
-Xtemp = Xzero;
+Xtemp = Xzero;
-for j = 1:L
+for j = 1:L
-Winc = sum(dW(R*(j-1)+1:R*j));
+Winc = sum(dW(R*(j-1)+1:R*j));
-Xtemp = Xtemp + Dt*lambda*Xtemp + mu*Xtemp*Winc;
+Xtemp = Xtemp + Dt*lambda*Xtemp + mu*Xtemp*Winc;
-Xem(j) = Xtemp;
+Xem(j) = Xtemp;
-end
+end
-plot([0:Dt:T],[Xzero,Xem],’r--*’), hold off
+plot([0:Dt:T],[Xzero,Xem],’r--*’), hold off
-xlabel(’t’,’FontSize’,12)
+xlabel(’t’,’FontSize’,12)
-ylabel(’X’,’FontSize’,16,’Rotation’,0,’HorizontalAlignment’,’right’)
+ylabel(’X’,’FontSize’,16,’Rotation’,0,’HorizontalAlignment’,’right’)
 emerr = abs(Xem(end)-Xtrue(end))