On the construction and analysis of some stochastic pseudo-first-order kinetic models

Time-inhomogeneous stochastic processes are constructed starting from the pseudo-first-order kinetic model by adopting two different approaches. For constant carrying capacity, the transition probability density functions and the related conditional moments are determined. The case in which the stochastic processes are restricted by a reflecting condition in the zero-state is also analyzed. Particular attention is paid to the first-passage time problem through a constant boundary for time-homogeneous processes and for time-inhomogeneous processes with proportional intensity functions. Various numerical computations and simulations are performed to compare the proposed models.