| dc.creator |
Charles, Wilson M. |
|
| dc.date |
2016-09-21T12:08:44Z |
|
| dc.date |
2016-09-21T12:08:44Z |
|
| dc.date |
2010 |
|
| dc.date.accessioned |
2018-03-27T08:58:05Z |
|
| dc.date.available |
2018-03-27T08:58:05Z |
|
| dc.identifier |
Charles, W., 2010. Application of coloured noise as a driving force in the stochastic differential equations. INTECH Open Access Publisher. |
|
| dc.identifier |
http://hdl.handle.net/20.500.11810/3787 |
|
| dc.identifier |
10.5772/46971 |
|
| dc.identifier.uri |
http://hdl.handle.net/20.500.11810/3787 |
|
| dc.description |
In this chapter we explore the application of coloured noise as a driving force to a set of
stochastic differential equations(SDEs). These stochastic differential equations are sometimes
called Random flight models as in A. W. Heemink (1990). They are used for prediction of
the dispersion of pollutants in atmosphere or in shallow waters e.g Lake, Rivers etc. Usually
the advection and diffusion of pollutants in shallow waters use the well known partial differential
equations called Advection diffusion equations(ADEs)R.W.Barber et al. (2005). These
are consistent with the stochastic differential equations which are driven by Wiener processes
as in P.E. Kloeden et al. (2003). The stochastic differential equations which are driven by
Wiener processes are called particle models. When the Kolmogorov’s forward partial differential
equations(Fokker-Planck equation) is interpreted as an advection diffusion equation,
the associated set of stochastic differential equations called particle model are derived and are
exactly consistent with the advection-diffusion equation as in A. W. Heemink (1990); W. M.
Charles et al. (2009). Still, neither the advection-diffusion equation nor the related traditional
particle model accurately takes into account the short term spreading behaviour of particles.
This is due to the fact that the driving forces are Wiener processes and these have independent
increments as in A. W. Heemink (1990); H.B. Fischer et al. (1979). To improve the behaviour of
the model shortly after the deployment of contaminants, a particle model forced by a coloured
noise process is developed in this chapter. The use of coloured noise as a driving force unlike
Brownian motion, enables to us to take into account the short-term correlated turbulent fluid
flow velocity of the particles. Furthermore, it is shown that for long-term simulations of the
dispersion of particles, both the particle due to Brownian motion and the particle model due
to coloured noise are consistent with the advection-diffusion equation. |
|
| dc.language |
en |
|
| dc.subject |
Brownian motion |
|
| dc.subject |
Stochastic differential equations |
|
| dc.subject |
Traditional particle models |
|
| dc.subject |
Coloured noise force |
|
| dc.subject |
Advection-diffusion equation |
|
| dc.subject |
Fokker-Planck equation |
|
| dc.title |
Application of Coloured Noise as a Driving Force in the Stochastic Differential Equations |
|
| dc.type |
Book chapter |
|