Sim.DiffProc (version 2.5)

JDP: Creating The Jacobi Diffusion Process (by Milstein Scheme)

Description

Simulation the jacobi diffusion process by milstein scheme.

Usage

JDP(N, M, t0, T, x0, theta, 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.

theta

constant positive.

output

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

Value

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

Details

The Jacobi diffusion process is the solution to the stochastic differential equation : $$dX(t) = -theta * (X(t) - 0.5)* dt + sqrt( theta*X(t)*(1-X(t))) * dW(t)$$ With -theta * (X(t) - 0.5) :drift coefficient and sqrt( theta*X(t)*(1-X(t))) :diffusion coefficient, W(t) is Wiener process, discretization dt = (T-t0)/N. For theta > 0. It has an invariant distribution that is uniform on [0,1].

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, DWP Double-Well Potential Model, GBM Model of Black-Scholes, HWV Hull-White/Vasicek Models, INFSR Inverse of Feller s Square Root models, PDP Pearson Diffusions Process, ROU Radial Ornstein-Uhlenbeck Process, diffBridge Diffusion Bridge Models, snssde Simulation Numerical Solution of SDE.

Examples

## Jacobi Diffusion Process 
## dX(t) = -0.05 * (X(t)-0.5)* dt + sqrt(0.05*X(t)*(1-X(t))) * dW(t),  
## One trajectorie
 JDP(N=1000,M=1,T=100,t0=0,x0=0,theta=0.05)