Hawkes Processes with Stochastic Excitations - Supplemental Materials
نویسندگان
چکیده
This proof is adapted from Dassios and Zhao (2013) to our setting. We first note that the intensity λ t increases by Y j at jump time T j. That is, the right limit λ T + j is equal to the left limit λ T − j plus Y j. Thus, after the j-th jump, the intensity λ t would follow λ t = λ T + j − a e −δ(t−Tj) + a, T j ≤ t < T j + S j+1 , where T j and λ T + j are observed at the j-th jump. Here S j+1 is the inter-arrival time for the (j + 1)-th jump: S j+1 = T j+1 − T j .
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