Small-time limit behavior of the probability that a Lévy process stays positive

• Published in: Кибернетика и системный анализ
• Date: 2016
• Main Author: Knopova, V.P.
• Format: Article
• Language: English
• Published: Інститут кібернетики ім. В.М. Глушкова НАН України 2016
• Subjects: Системный анализ
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/133691
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Small-time limit behavior of the probability that a Lévy process stays positive / V.P. Knopova // Кибернетика и системный анализ. — 2016. — Т. 52, № 3. — С. 164-169. — Бібліогр.: 8 назв. — англ.

In the paper, we find analytically the upper and lower limits (as the time parameter tends to zero) of the probability that the Lévy process staring at 0 stays positive. We confine ourselves to the situation where the real and imaginary parts of the characteristic function are regularly varying at i...