The proof of a theorem that allows one to construct deterministic evolution equations from a set, with two subsets, containing two types of discrete stochastic evolution equation is developed. One subset evolves Markovianly and the other non-Markovianly. As an illustrative example, the...

The deterministic evolution equations of classical as well as quantum mechanical models are derived from a set of stochastic evolution equations after taking an average over realizations using a theorem. Examples are given that show that deterministic quantum mechanical evolution equations,...

The continuum evolution equations are derived from updating rules for three classes of stochastic models. The first class corresponds to models whose stochastic continuum equations are of the Langevin type obtained after carrying out a “local average” known as coarse-graining. The second...

It is proved that it is possible to obtain continuum deterministic and stochastic evolution equations from a set of discrete stochastic rules after an average over realizations and over near neighbors or coarse graining on the dynamical variables, respectively. Examples are given that allow us...

In this paper the kinetic of dissociative adsorption of dimers followed by associative desorption is analyzed. The coupled differential equations which describe the kinetics of the process were obtained by applying the so-called local evolution rules. Particular interest presents the...

Deterministic evolution equations of classical as well as quantum mechanical models are derived from a set of non-Markovian stochastic evolution equations after an average over realization using a theorem. Examples are given, show that deterministic differential equations that contain...

The analytical continuous equations for the Tang and Leschhorn (Phys. Rev. A 45 (1992) R8309) and the Buldyrev et al. (Phys. Rev. A 45 (1992) R8313) models are derived from the microscopic rules using a regularization procedure. As was shown in a previous paper (Phys. Rev. E 62 (2000) 6970) the...