Non-Homogeneous Poisson Process (NPHH)

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1. Properties:

  • N(0) = 0
  • N(t) has independent increments
  • Pr{N(t+h) - N(t)} = lambda(t)h + o(h)
  • Pr{N(t+h)-N(t) geq 2} = o(h)
Notes:
  • This is like a Poisson process, without the stationary assumption
A process with the above properties is a NHPP with intensity (or rate) function lambda(t)

2. Definition: 

The mean value function (for a NHPP) is

m(t) = int^t_0 lambda(u) du

3. Key Properties: 

  • For a NHPP, N(s+t) – N(s) is a Poisson random variable with mean m(s+t) - m(s)

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