Simulating Stochastic Differential equations

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jacob Mitch
jacob Mitch 2019-11-14
编辑： jacob Mitch 2019-11-14
I am just learning about Stochastic differential equations if I have a SDE of dX(t) = -μ*X(t)*dt + σ*W(t) X0=x0>0 where W(t) is the Wiener process and I am trying to simulate it using
X(n+1)=X(n)−μX(n)∆t+σ*sqrt(∆t)*ηn, where ∆t = T /N :and ηn ∼ N (0, 1) normal distribution
So far I am here but not sure how to proceed and if I am simulating correctly and how the initial condition X0=x0>0 comes into it
dt_large = T / N;
t = linspace ( 0, T, N + 1 );
x = zeros ( 1, N + 1 );
x(1) = x0;
for j = 1 : n
dw = sqrt ( dt_large ) * randn ( 1, r );
x(j+1) = x(j) - x(j)* mu*dt_large + sigma * sum ( dw(1:r) );
end

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