Sim.DiffProc (version 2.5)

DWP: Creating Double-Well Potential Model (by Milstein Scheme)

Description

Simulation double-well potential model by milstein scheme.

Usage

DWP(N, M, t0, T, x0, output = FALSE)

Arguments

N

size of process.

M

number of trajectories.

t0

initial time.

T

final time.

x0

initial value of the process at time t0.

output

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

Value

• data.frame(time,x) and plot of process.

Details

This model is interesting because of the fact that its density has a bimodal shape. The process satisfies the stochastic differential equation : $$dX(t) = ( X(t) - X(t)^3) * dt + dW(t)$$ With (X(t) - X(t)^3) :drift coefficient and 1 is diffusion coefficient, W(t) is Wiener process,and the discretization dt = (T-t0)/N. This model is challenging in the sense that the Milstein approximation.

See Also

CEV Constant Elasticity of Variance Models, CIR Cox-Ingersoll-Ross Models, CIRhy modified CIR and hyperbolic Process, CKLS Chan-Karolyi-Longstaff-Sanders Models, GBM Model of Black-Scholes, HWV Hull-White/Vasicek Models, INFSR Inverse of Feller s Square Root models, JDP Jacobi Diffusion Process, PDP Pearson Diffusions Process, ROU Radial Ornstein-Uhlenbeck Process, diffBridge Diffusion Bridge Models, snssde Simulation Numerical Solution of SDE.

Examples

## Double-Well Potential Model 
## dX(t) = (X(t) - X(t)^3) * dt + dW(t)
## One trajectorie
DWP(N=1000,M=1,T=1,t0=0,x0=1)