Sim.DiffProc (version 2.5)

tho_M2: Simulation The First Passage Time FPT For Attractive Model(S >= 2,Sigma)

Description

simulation M-sample for the first passage time "FPT" for attractive model(S >= 2,Sigma).

Usage

tho_M2(N, M, t0, T, R0, v, K, s, Sigma, Output = FALSE,
       Methods = c("Euler", "Milstein", "MilsteinS", 
                   "Ito-Taylor", "Heun", "RK3"), ...)

Arguments

N

size of the diffusion process.

M

size of the FPT.

t0

initial time.

T

final time.

R0

initial value of the process at time t0 ,(R0 > 0).

v

threshold. see detail.

K

constant K > 0.

s

constant s >= 2.

Sigma

constant Sigma > 0.

Output

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

Methods

method of simulation ,see details snssde.

...

Value

• M-sample for FPTT.

Details

Using Ito transform, it is shown that the Radial Process R(t) with R(t)=||(X(t),Y(t))|| is a markovian diffusion, solution of the stochastic differential equation one-dimensional: $$dR(t) = ((0.5 * Sigma^2 * R(t)^(S-1) - K)/ R(t)^S )* dt + Sigma* dW(t)$$ We take interest in the random variable FPT "first passage time", is defined by : $$FPT = inf(t>=0 \ R(t) <= v="" )$$<="" em=""> with v is the threshold. 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

AnaSimFPT Simulation The First Passage Time FPT For A Simulated Diffusion Process.

Examples

tho_M2(N=1000, M=50, t0=0, T=1, R0=2, v=0.05, K=3,s=2,
        Sigma=0.3,Output = FALSE,Methods="Euler")