Continuous-time random walks at all times.

Continuous-time random walks (CTRW) play an important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on dynamics at long times. We present a new theoretical approach, based on generalized master equations picture, which allowed us to obtain explicit expressions for Laplace transforms for all dynamic quantities for different CTRW models. This theoretical method leads to the effective description of CTRW at all times. Specific calculations are performed for homogeneous, periodic models and for CTRW with irreversible detachments. The approach to stationary states for CTRW is analyzed. Our results are also used to analyze generalized fluctuations theorem.