Suprema of compound Poisson processes with light tails
نویسندگان
چکیده
منابع مشابه
Extremes of Lévy Processes with Light Tails
Let X(t) t ≥ 0 , X(0) = 0, be a Lévy process with spectral Lévy measure ρ. Assuming that ρ((−∞, 0)) < ∞ and the right tail of ρ is light, we show that in the presence of Brownian component P „ sup 0≤t≤1 X(t) > u « ∼ P (X(1) > u) as u → ∞. In the absence of Brownian component these tails are not always comparable. An example of Lévy process of the type X(t) = B(t) + Z(t), where B(t) is a Brownia...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2000
ISSN: 0304-4149
DOI: 10.1016/s0304-4149(00)00039-9