Limit theorems for the process of exceedances in large populations.
Rahimov, Ibrahim, Hasan, Husna (2000)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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The density of real-valued Lévy processes is studied in small time under the assumption that the process has many small jumps. We prove that the real line can be divided into three subsets on which the density is smaller and smaller: the set of points that the process can reach with a finite number of jumps (Δ-accessible points); the set of points that the process can reach with an infinite number of jumps (asymptotically Δ-accessible points); and the set of points that the process...
Process-level large deviations for nonlinear Hawkes point processes
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In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.