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math.PR2019
Functional Limit Theorems for Marked Hawkes Point Measures
Ulrich Horst, Wei Xu
This paper establishes a functional law of large numbers and a functional central limit theorem for marked Hawkes point measures and their corresponding shot noise processes. We pr…
math.PR2018
Scaling Limits for Crump-Mode-Jagers Processes with Immigration via Stochastic Volterra Equations
Wei Xu
In this paper, we firstly give a reconstruction for Crump-Mode-Jagers processes with immigration as solutions to a class of stochastic Volterra integral equations, which offers us…