Gaussian approximation and moderate deviations of poisson shot noises with application to compound generalized hawkes processes

HIGHLIGHTS

• What: As a main application, the authors provide moderate deviations, Bernstein-type concentration inequalities, and normal approximation bounds with Cramér correction term for sequences of compound sums, which extend Poisson cluster and Hawkes point processes (see Corollaries 2, 4, and 6). The authors provide bounds for the Wasserstein and Kolmogorov distances (hereafter denoted by dW and dK, respectively; see Section 4.1 for a formal definition of these probability metrics) between a standard Gaussian random variable G and S(C) - ES(C), T(C):=√ Var(S(C)) https://doi.org/10.1017/apr.2024.51 Published . . .
  

   

  

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