Shot-noise processes with logarithmic response functions converge weakly to Hadamard fractional Brownian motion, a process with Brownian marginals and fractional long memory of reduced intensity.
Kingman, Poisson Processes, Oxford Studies in Probability, Clarendon Press
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Shot-noise processes with logarithmic response function and their scaling limits
Shot-noise processes with logarithmic response functions converge weakly to Hadamard fractional Brownian motion, a process with Brownian marginals and fractional long memory of reduced intensity.