NonHomogeneousPoissonProcess
NonHomogeneousPoissonProcess represents a Poisson process with time-dependent intensity
\(\lambda(t)\) and mean function
\[m(t)=\int_0^t \lambda(x)\,dx.\]
Constructor
NonHomogeneousPoissonProcess(intensity_function, mean_function=None)
Parameters
| Parameter | Description |
|---|---|
intensity_function |
Callable intensity \(\lambda(t)\). |
mean_function |
Optional callable mean function \(m(t)\). |
Properties
| Property | Meaning |
|---|---|
intensity_function |
The intensity callable. |
mean_function |
The mean-function callable. |
Methods
mean(t)— evaluate \(m(t)\).count_probability(n, t)— compute the count probability at timet.increment_probability(n, s, t)— compute the increment probability on[s, t].simulate(t_max, rng=None)— generate events up to a finite horizon.
Example
from stochx.stochastic import NonHomogeneousPoissonProcess
process = NonHomogeneousPoissonProcess(
intensity=lambda t: 1.0 + t,
mean_function=lambda t: t + 0.5 * t**2,
)
print(process.intensity_function(2.0))
print(process.mean(2.0))
print(process.count_probability(2, 2.0))
Related API
PoissonProcess provides the homogeneous constant-rate case.