Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function
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Publication:6509265
arXiv2303.11964MaRDI QIDQ6509265
Jorge Ignacio González Cázares, Feng Lin, Aleksandar Mijatović
Abstract: We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non-increasing absolutely continuous function. We prove that the running time of our algorithm has finite exponential moments and provide bounds on its expected running time with explicit dependence on the characteristics of the process and the initial value of the function. The expected running time grows at most cubically in the stability parameter (as it approaches either or ) and is linear in the tempering parameter and the initial value of the function. Numerical performance, based on the implementation in the dedicated GitHub repository, exhibits a good agreement with our theoretical bounds. We provide numerical examples to illustrate the performance of our algorithm in Monte Carlo estimation.
Has companion code repository: https://github.com/jorgeignaciogc/FirstPassageTemperedStable.jl
Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Exact distribution theory in statistics (62E15) Monte Carlo methods (65C05)
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