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math.PR2025
Functional Laws of Large Numbers for Marked Hawkes Processes and Compound Marked Hawkes Processes
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz iewȩgłowski +1
We give functional laws of large numbers for a class of marked Hawkes processes and marked compound Hawkes processes with a general mark space. Our results provide some complement…
math.PR2025
Loglinear Hawkes processes: existence, nonexplosion, stability and moment bounds
Tomasz R. Bielecki, Jacek Jakubowski, Matthias Kirchner +1
This paper discusses a special class of nonlinear Hawkes processes, where the rate function is the exponential function. We call these processes loglinear Hawkes processes. Such pr…