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Just keep in mind that Gaussian marginals with Gaussian copula is nothing more than the multivariate Gaussian distribution (details e.g. here). For t-marginals with t-copula (with the same degree of freedom) you get the multivariate t-distribution. Both multivariate distributions are characterized by their covariance matrix. The t-distribution has the ...

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You can express the Normal distribution by Sklar's Theorem in terms of Gaussian Marginals and Gaussian Copula as follows: $$F(x_1,...,x_n)=C(F(x_1),...,F(x_n))=C^{Gau}(N(x_1),...,N(x_n))$$ So the distribution equals the copula function with the respective inverse marginals as arguments. You can aswell combine any types of Copula and (continuous) different ...

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As you know, simulating AR(1) is to simulate the distributed error path. Assume the bivariate errors distributed $\sim F(x),\sim F(y)$ with copula $C(u,v)$ to model their dependence. Then the bivariate joint error distribution is given by Sklar's theorem: $$F(x,y)=C(F(x),F(y))$$ You can simulate from this distribution using Conditional Sampling: To ...

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0/ Let's me use more common notations to avoid misunderstanding. We will consider $B_t^x$ and $B_t^y$ - two correlated Brownian motions, e.g. $<dB_t^x,dB_t^y>=\rho dt$. Just to recall, Ito's process: $$X_t = X_0 + \int_0^t \mu(s,\omega) ds + \int_0^t \sigma(s,\omega) dB_s^x\\ dX_t=\mu(t,\omega) dt + \sigma(t,\omega) dB_t^x$$ 1/ Single BMs: ...

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