Self-similar processes as weak limits of a risk reserve process

• Autorzy: Burnecki K.
• Języki publikacji: EN

Abstrakty

EN

Self-similar processes are closely connected with limit theorems for identical and in general strongly dependent variables. Moreover, since they allow heavytailed distributions and provide an additional “adjusting” parameter H, they appear to be interesting in the area of risk models. In this paper we prove that only self-similar processes with stationary increments appear naturally as weak limits of a risk reserve process, and conversely every finite mean H-self-similar process with stationary increments for 0 < H ≤ 1 can result as the weak approximation. A lower bound for general self-similar processes with drift is also provided.

Słowa kluczowe

EN

self-similar process; risk models; stationary increments

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 261--272
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Burnecki K.

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Bibliografia

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