Public Function Poisson_process(ByVal lambda, ByVal N, ByVal start, ByVal fin, Optional vect0 As Double)
'Simulate a Poisson process with parameter lambda
Dim vect(), t(), sum() As Double
Dim i, compte As Long
Dim dt As Double

ReDim vect(0 To N)
ReDim t(0)
ReDim sum(0)

dt = (fin - start) / N

vect(0) = vect0
t(0) = 0
sum(0) = t(0)

i = 0
While (sum(i) <= fin)
    ReDim Preserve sum(0 To i + 1)
    ReDim Preserve t(0 To i + 1)
    t(i + 1) = expdistrib(lambda)
    sum(i + 1) = sum(i) + t(i + 1)
    i = i + 1
Wend

nb = i - 1

For i = 1 To N
    compte = 0
    somme = 0
    j = 0
    
    While ((sum(compte) <= dt * i) And (compte <= nb))
        compte = compte + 1
    Wend

    vect(i) = compte - 1
Next i
Poisson_process = vect
End Function