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math.PR2023
Efficient evaluation of joint pdf of a Lévy process, its extremum, and hitting time of the extremum
Svetlana Boyarchenko, Sergei Levendorskii
For Lévy processes with exponentially decaying tails of the Lévy density, we derive integral representations for the joint cpdf of (the process, its supre…
math.PR2022
Efficient evaluation of expectations of functions of a stable Lévy process and its extremum
Svetlana Boyarchenko, Sergei Levendorskiĭ
Integral representations for expectations of functions of a stable Lévy process and its supremum are derived. As examples, cumulative probability distribution function…
math.PR2022
Efficient evaluation of expectations of functions of a Lévy process and its extremum
Svetlana Boyarchenko, Sergei Levendorskiĭ
We prove simple general formulas for expectations of functions of a Lévy process and its running extremum. Under additional conditions, we derive analytical formulas using the Four…