We give a general inequality for the total variation distance between a Poisson distributed random variable and a first order stochastic integral with respect to a point process with stochastic intensity, constructed by embedding in a bivariate Poisson process. We apply this general inequality to first order stochastic integrals with respect to a class of nonlinear Hawkes processes, which is of interest in queueing theory, providing explicit bounds for the Poisson approximation, a quantitative Poisson limit theorem, confidence intervals and asymptotic estimates of the moments.
Poisson approximation of point processes with stochastic intensity, and application to nonlinear Hawkes processes
Torrisi;Giovanni Luca
2017
Abstract
We give a general inequality for the total variation distance between a Poisson distributed random variable and a first order stochastic integral with respect to a point process with stochastic intensity, constructed by embedding in a bivariate Poisson process. We apply this general inequality to first order stochastic integrals with respect to a class of nonlinear Hawkes processes, which is of interest in queueing theory, providing explicit bounds for the Poisson approximation, a quantitative Poisson limit theorem, confidence intervals and asymptotic estimates of the moments.File in questo prodotto:
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