############# geometric Brownian Motion #####
require(sde)
set.seed(123)

d <- expression( x ) 
s <- expression( 0.5*x ) 

X <- sde.sim(X0=10,drift=d, sigma=s)
plot(X,main="β˶")

##########  # Ornstein-Uhlenbeck process##########
require(sde)
set.seed(123)

d <- expression(-5 * x)
s <- expression(3.5) 

X <- sde.sim(X0=10,drift=d, sigma=s) 
plot(X,main="Ornstein-Uhlenbeck")


############## # Cox-Ingersoll-Ross  ########
require(sde)
set.seed(123)

d <- expression( 6-3*x ) 
s <- expression( 2*sqrt(x) ) 

X <- sde.sim(X0=10,drift=d, sigma=s) 
plot(X,main="Cox-Ingersoll-Ross")
