Distribution of Overjump Functionals of a Semicontinuous Homogeneous Process with Independent Increments
We establish relations for the distributions of functionals associated with an overjump of a process ξ(t) with continuously distributed jumps of arbitrary sign across a fixed level x > 0 (including the zero level x = 0 and infinitely remote level x → ∞). We improve these relations in the case...
Збережено в:
| Дата: | 2002 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2002
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4067 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We establish relations for the distributions of functionals associated with an overjump of a process ξ(t) with continuously distributed jumps of arbitrary sign across a fixed level x > 0 (including the zero level x = 0 and infinitely remote level x → ∞). We improve these relations in the case where the distributions of maxima and minima of ξ(t) may have an atom at zero. The distributions of absolute extrema of semicontinuous processes are defined in terms of these atomic probabilities and the cumulants of the corresponding monotone processes. |
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