Given $X_t$ a Levy process and $\Delta$ an interval of time, I have to compute the Wiener-Hopf factorization $\Phi_+$$\Phi_-$ of $$\Phi(u,q)=1-q\mathbf{E}[e^{iuX_{\Delta}}]=1-q\varphi(u)=\Phi_+(u,q)\Phi_-(u,q)$$ So given $\varphi$ the characteristic function of $X_\Delta$, I have to find $\Phi_+$ and $\Phi_-$, not necessarily in an explicit form. Any help is appreciated.


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