Sim.DiffProc (version 2.5)

RadialP2D_1: Two-Dimensional Attractive Model Model(S = 1,Sigma)

Description

Simulation 2-dimensional attractive model (S = 1).

Usage

RadialP2D_1(N, t0, Dt, T = 1, X0, Y0, v, K, Sigma, Output = FALSE)

Arguments

N

size of process.

t0

initial time.

Dt

time step of the simulation (discretization).

T

final time.

X0

initial value of the process X(t) at time t0.

Y0

initial value of the process Y(t) at time t0.

v

threshold. 0 < v < sqrt(X0^2 + Y0 ^2)

K

constant K > 0.

Sigma

constant Sigma > 0.

Output

if Output = TRUE write a Output to an Excel (.csv).

Value

• data.frame(time,X(t),Y(t)) and plot of process 2-D.

Details

The attractive models is defined by the system for stochastic differential equation Two-dimensional : $$dX(t) = (-K * X(t)/(sqrt(X(t)^2 + Y(t)^2))^(S+1) )* dt + Sigma* dW1(t)$$ $$dY(t) = (-K * Y(t)/(sqrt(X(t)^2 + Y(t)^2))^(S+1) )* dt + Sigma* dW2(t)$$ dW1(t) and dW2(t) are brownian motions independent. If S = 1 (ie M(S=1,Sigma)) the system SDE is : $$dX(t) = (-K * X(t)/(X(t)^2 + Y(t)^2) )* dt + Sigma* dW1(t)$$ $$dY(t) = (-K * Y(t)/(X(t)^2 + Y(t)^2) )* dt + Sigma* dW2(t)$$ For more detail consulted References.

References

1. K.Boukhetala, Estimation of the first passage time distribution for a simulated diffusion process, Maghreb Math.Rev, Vol.7, No 1, Jun 1998, pp. 1-25.
2. K.Boukhetala, Simulation study of a dispersion about an attractive centre. In proceedings of 11th Symposium Computational Statistics, edited by R.Dutter and W.Grossman, Wien , Austria, 1994, pp. 128-130.
3. K.Boukhetala,Modelling and simulation of a dispersion pollutant with attractive centre, Edited by Computational Mechanics Publications, Southampton ,U.K and Computational Mechanics Inc, Boston, USA, pp. 245-252.
4. K.Boukhetala, Kernel density of the exit time in a simulated diffusion, les Annales Maghrebines De L ingenieur, Vol , 12, N Hors Serie. Novembre 1998, Tome II, pp 587-589.

See Also

snssde2D, PredCorr2D, RadialP2D_1PC, RadialP3D_1, tho_M1, fctgeneral, hist_general, Kern_meth.

Examples

RadialP2D_1(N=1000, t0=0, Dt=0.001, T = 1, X0=2, Y0=1, v=0.3, 
             K=3, Sigma=0.2, Output = FALSE)