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math.NA2020★ 3 cited
Theoretical analysis and simulation methods for Hawkes processes and their diffusion approximation
Julien Chevallier, Anna Melnykova, Irene Tubikanec
Oscillatory systems of interacting Hawkes processes with Erlang memory kernels were introduced in Ditlevsen (2017). They are piecewise deterministic Markov processes (PDMP) and can…
math.NA2020★ 1 cited
Qualitative properties of numerical methods for the inhomogeneous geometric Brownian motion
Irene Tubikanec, Massimiliano Tamborrino, Petr Lansky +1
We provide a comparative analysis of qualitative features of different numerical methods for the inhomogeneous geometric Brownian motion (IGBM). The conditional and asymptotic mean…