I am reading this paper "OPTION PRICING IN A REGIME-SWITCHING MODEL USING THE FAST FOURIER TRANSFORM" wrote by R. H. LIU, Q. ZHANG, AND G. YIN.
In this paper, the equation (2.3) is: \begin{equation} X(t)=\int_{0}^{t}\left(\mu(\alpha(s))-\frac{1}{2} \sigma^{2}(\alpha(s))\right) d s+\int_{0}^{t} \sigma(\alpha(s)) d \widetilde{B}(s), \quad t \geq 0 . \end{equation} where $\alpha(t)$ is a finite-state continuous time Markov chain with state space $\mathcal{M} = \{1,\cdots,m\}$.
Then, given $\mathcal{F}_T$ (the $\sigma$-algebra generated by the Markov chain $α(t), \, 0 \leq t \leq T$), why $X(T)$ is Gaussian? (which the writer stated on page 6).