Introduction - Noise-induced Phenomena in the Environmental Sciences - page 6

noise (i.e., the so-called Ornstein-Uhlenbeck process) presented in the next chapter. With
this assumption the bivariate system composed of the state variable

ξ
becomes Markovian, and some analytical representations of the stochastic dynamics can be
obtained.
Case with

φ and the noise

τ s /τ n

1: In this case the system responds very quickly to the noise forcing,
thereby adjusting (almost) instantaneously to the random forcing. In other words, the state
variable

φ is always in equilibrium with the noise term [i.e., d φ/ d t 0]. In these conditions

we can use the so-called adiabatic elimination of the φ variable, whereby the dynamics of

φ are described as f ( φ ) + g ( φ ) ξ = 0 and the probabilistic properties of φ are derived from

those of the noise.

In the following chapters we consider different types of noise, including the case
of both white and colored noise as well as continuous and intermittent noises. We
review the major properties of each type of noise as well as their possible use in the
development of stochastic models of environmental systems. To this end, we use a
number of examples and case studies to show the possible impact of both additive
and multiplicative noise on environmental dynamics.