  Continuous-time random walks (CTRW) play important role in understanding of a
wide range of phenomena. However, most theoretical studies of these models
concentrate only on stationary-state dynamics. We present a new theoretical
approach, based on generalized master equations picture, that 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.
