If I have this type of stochastic differential equation : $ dX(t) = A(X(t),t)\ dt +B(X(t),t)\ dW(t) + C(X(t),t)\ dP(t) $ With $ \begin{align} dW(t)& : \text{A wiener process}\\ dP(t)& : \text{A Poisson process with parameter }\Lambda\\ A,B,C& : \text{Smooth functions} \end{align} $ and I want to transform it to this type of stochastic differential equations: $ dX(t) = F(X(t),t)\ dt + G(X(t),t)\ dL(t)\\ $ with $ \begin{align} L(t)& : \text{An }\alpha\text{-stable Levy process} \end{align} $ I was trying to identify the relations between the coefficients and parameters. Could some one tell me if I can use the development of a Levy process to a Brownian motion, a drift and a poisson process to find a relation between those two equations ?
I wanted to use it in the case $F$ and $G$ are constants.
Thank you.
Kind regards