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On a Small-Time Limit Behaviorof the Probability That a Lévy Process Stays Positive

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Abstract

In this paper, we find analytically the upper and lower limits (as the time parameter tends to zero) of the probability that a Lévy process starting at 0 stays positive. We confine ourselves to the case where the real and imaginary parts of the characteristic function regularly vary at infinity. In this case we can calculate the bound and sometimes the exact values of the respective upper and lower limits.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. P. Knopova

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  1. V. P. Knopova
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Correspondence to V. P. Knopova.

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Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2016, pp. 164–169.

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Knopova, V.P. On a Small-Time Limit Behaviorof the Probability That a Lévy Process Stays Positive. Cybern Syst Anal 52, 475–480 (2016). https://doi.org/10.1007/s10559-016-9848-8

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  • DOI: https://doi.org/10.1007/s10559-016-9848-8

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