Multivariate formulation of transient stochastic dynamics

The objective of this paper is to generalize the formulation, reported in previous works, which we term as standard formulation of quasideterministic approach, to multivariate unstable systems. As usual, the new formalism is connected with the nonlinear relaxation times, to characterize the transient stochastic dynamics of those unstable systems which are governed by a multivariate Langevin-type equation. The generalized method is applied to study two analytical models in two and three variables in order to obtain explicit results and calculate the time scale associated with the decay of the unstable state of such systems. The theoretical formalism constitutes an alternative method to study some physical systems in two and three varibles. The laser systems represent one possibility in this theoretical context.