title: Moment evolution and level-crossing statistics in dichotomous and multilevel flows with time-dependent control parameters.
abstract: We study the dynamics of the first two moments and of threshold crossings by the stochastic trajectory in dichotomous diffusion x=xi(t), where xi(t) is a dichotomous Markov process. The transition rate of the latter is regarded as a control parameter and allowed to have specified time variations. The stabilizing or destabilizing effect of this variation is demonstrated, and qualitative changes in the statistical properties of the system are shown to occur. The analysis is then extended to linear dichotomous flow, and to a generalization of dichotomous diffusion in which x is driven by a multilevel Markov noise.
authors.affiliation: Centre for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Boulevard du Triomphe, 1050 Brussels, Belgium.
authors.forename: G
authors.initials: G
authors.lastname: Nicolis
authors.forename: V
authors.initials: V
authors.lastname: Balakrishnan
authors.forename: C
authors.initials: C
authors.lastname: Nicolis