In this dissertation, we develop multivariate Dickman distribution and explore its properties. In addition, we utilize the Dickman distribution to approximate the small jumps of Levy processes of finite variation, building upon the work presented in Covo(2009) for the univariate case. Our central theorem establishes that the limit distribution of an appropriately transformed truncated Levy process with finite variation is the Dickman distribution. We also provide equivalent conditions to further characterize this result. Drawing inspiration from this, we partition the Levy process into small jumps and large jumps. Small jumps are effectively approximated by the Dickman distribution, while the remaining large jumps follow a compound Poisson distribution. We then apply this to simulate Levy processes within the generalized multivariate gamma class. Further, we extend our findings to stochastic integral processes particularly related to Ornstein-Uhlenbeck (OU) processes. Our investigation encompasses two scenarios: the truncated OU process and the OU process driven by a truncated Levy process. In general, employing the same transformation outlined in our main theorem, we observe that the limit distribution of the truncated OU process aligns with a multivariate Dickman distribution. Notably, for the OU process with a truncated driving process, the limit distribution remains consistent with that of the OU process with a truncated driving process having the multivariate Dickman distribution.