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Sim.DiffProc (version 2.5)

FBD: Feller Branching Diffusion

Description

Simulation the Feller Branching diffusion.

Usage

FBD(N, M, t0, T, x0, mu, sigma, 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.
mu
constant (mu * X(t) :drift coefficient).
sigma
constant positive (sigma * sqrt(X(t)) :diffusion coefficient).
output
if output = TRUE write a output to an Excel (.csv).

Value

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

Details

The Feller Branching diffusion model also derives directly from the linear drift class, the discretization dt = (T-t0)/N. A simple branching process is a model in which individuals reproduce independently of each other and of the history of the process. The continuous approximation to branching process is the branching diffusion. It is given by the stochastic differential equation for the population size X(t), 0 < X(t) < +Inf : $$dX(t) = mu * X(t)* dt + sigma * sqrt(X(t)) *dW(t)$$ with mu * X(t) :drift coefficient and sigma * sqrt(X(t)) :diffusion coefficient, W(t) is Wiener process.

References

Fima C Klebaner. Introduction to stochastic calculus with application (Second Edition), Imperial College Press (ICP), 2005.

See Also

SLVM Stochastic Lotka-Volterra, WFD Wright-Fisher Diffusion.

Examples

Run this code
FBD(N=1000,M=1,t0=0,T=1,x0=1,mu=2,sigma=0.5,output=FALSE)

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