Weighted Limit Theorems for Continuous-Time Vector Martingales with Explosive and Mixed Growth

In this article, we establish the almost-sure central limit theorem (ASCLT) for a quasi-left continuous vector martingale with explosive and mixed (regular and explosive) growth. We also prove a quadratic extension and establish several new central limit theorems associated with the obtained ASCLT. Finally, we study the problem of parameter estimation in the particular case of multidimensional diffusion processes, which illustrates in a concrete manner the use of our results.