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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 20, Fasc. 2,
pages 261 - 272
 

SELF-SIMILAR PROCESSES AS WEAK LIMITS OF A RISK RESERVE PROCESS

Krzysztof Burnecki

Abstract: Self-similar processes are closely connected with limit theorems for identical and in general strongly dependent variables. Moreover, since they allow heavy-tailed 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.

1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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