FUNCTION PoissonProcess,t,lambda,p
;+
; S=PoissonProcess(t,lambda,p)
; divides the interval [0,t] into intervals of size
; deltaT=p/lambda where p is sufficiently small so that
; the Poisson assumptions are satisfied. The value of
; p may be specified by the third positional variable.
; If it is not provided, it is set to the default value
; p=0.1.
;
; The interval (0,t) is divided into n=t*lambda/p intervals
; and the number of events in the interval (0,k*deltaT) is
; returned in the array S. The maximum length of S is 10000.
;
; USAGE
; S=PoissonProcess(10,1,0.1)
; Plot,S
; FOR m=1,10 DO OPLOT,PoissonProcess(10,1,0.1)
;
; The above generate a number of overlayed plots of the process.
;
; Harvey Rhody
; March, 2000
;-

NP=N_PARAMS()
IF NP LT 3 THEN p=0.1
n=lambda*t/p
;u=FIX(RANDOMN(SEED,n,BINOMIAL=[1,p])>0)
u=Randomn(seed,n,Poisson=p)
s=INTARR(n+1)
FOR k=1,n DO s[k]=s[k-1]+u[k-1]
RETURN,s
END