Stochastic Differential Equations and simulation

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Mari Alqarni
Mari Alqarni 2016-2-9
I am working on stochastic differential equations for the first time. I am looking to simulate and solve a stochastic differential equations in two dimensions.
The model is as follows:
dp=F(t,p)dt+G(t,p)dW(t) where:
p is a 2-by-1 vector: p=(theta(t); phi(t)) F is a column vector: F=(sin(theta)+Psi* cos(phi); Psi* cot(theta)*sin(phi)) G is a 2-by-2 matrix: G=(D 0;0 D/sin(theta)) Psi is a parameter and D is the diffusion constant I wrote code as follows:
function MDL=gyro_2dim(Psi,D)
% State vector: p = [theta;phi];
F = @(t,p)[sin(p(1))+Psi.*cos(p(2))-D.*cot(p(1));
Psi.*cot(p(1)).*sin(p(2))]; % Drift
G = @(t,p)[D 0;
0 D./sin(p(1))]; % Diffusion
MDL = sde(F,G);
Then I call the function with the following script:
params.t0 = 0; % start time of simulation
params.tend = 20; % end time
params.dt =0.1; % time increment
D=0.1;
nPeriods=10; % # of simulated observations
Psi=1;
MDL=gyro_2dim(Psi,D);
[S,T,Z]=simulate(MDL, nPeriods,'DeltaTime',params.dt);
plot(T,S)
When I run the code, I receive this error message:
Drift rate invalid at initial conditions or inconsistent model dimensions.
Any idea how to fix this error?

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