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Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse topologies and stable dynamics are fundamental features of many real-world continuous-time (CT) networks. Given that usually only a partial set of nodes are able to observe, in this paper, we consider linear CT systems to depict networks since they can model unmeasured nodes via transfer functions. Additionally, measurements tend to be noisy and with low and varying sampling frequencies. For this reason, we consider CT models since discrete-time approximations often require fine-grained measurements and uniform sampling steps. The developed method applies dynamical structure functions (DSFs) derived from linear stochastic differential equations (SDEs) to describe networks of measured nodes. A numerical sampling method, preconditioned Crank-Nicolson (pCN), is used to refine coarse-grained trajectories to improve inference accuracy. The convergence property of the developed method is robust to the dimension of data sources. Monte Carlo simulations indicate that the developed method outperforms state-of-the-art methods including group sparse Bayesian learning (GSBL), BINGO, kernel-based methods, dynGENIE3, GENIE3, and ARNI. The simulations include random and ring networks, and a synthetic biological network. These are challenging networks, suggesting that the developed method can be applied under a wide range of contexts, such as gene regulatory networks, social networks, and communication systems.