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You should review your definition of what a differential equation is: dSt= mu*St*dt + sqrt(vt)*St*dW1t + Jt*dQt it means simply that S_t+1=St + mu*St*dt + sqrt(Vt)*St*(W_t+1-Wt) + Jt*(Q_t+1-Q_t)


...this technique works only when returns are generated from normal distributions? Yes and no. Multiplying them by $C$ will produce the correlation that you wanted, but it won't preserve the distribution in general. Remember that when we apply $C$ to a vector of i.i.d. random variables $\boldsymbol{x}$ that the resultant vector element is $\sum_j C_{ij}x_j$,...


They are independent. The point is that $y$ is derived from your easily sampled distribution $g$ randomly. Now you have a random test (via $v$) that decides whether to accept $y$ or not as part of the random sample of the harder to sample $f$. The procedure uses $M$ in the accept-reject method and whilst you can derive conservative estimates with $M$ quite ...

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