Sim.DiffProc (version 2.1)

Hyproc: Creating The Hyperbolic Process (by Milstein Scheme)

Description

Simulation hyperbolic process by milstein scheme.

Usage

Hyproc(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 2007.

Value

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

Details

A process X satisfying : $$dX(t)=(-theta\ast X(t)/sqrt(1+X(t{)}^2))\ast dt+dW(t)$$ With (-theta*X(t)/sqrt(1+X(t)^2)) :drift coefficient and 1 :diffusion coefficient, W(t) is Wiener process, discretization dt = (T-t0)/N. Constraints: theta > 0.

See Also

Hyprocg General Hyperbolic Diffusion, CIRhy modified CIR and hyperbolic Process, snssde Simulation Numerical Solution of SDE.

Examples

## Hyperbolic Process 
## dX(t) = (-2*X(t)/sqrt(1+X(t)^2)) *dt + dW(t)
## One trajectorie
Hyproc(N=1000,M=1,T=100,t0=0,x0=3,theta=2)