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Teoriya Veroyatnostei i ee Primeneniya, 2000, Volume 45, Issue 2, Pages 380–386
DOI: https://doi.org/10.4213/tvp471 (Mi tvp471) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

On a maximum of stable Lévy processes

G. M. Molchanab

a International Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS
b Observatoire de la Côte d'Azur
Full-text PDF (385 kB) Citations (2)
DOI: https://doi.org/10.4213/tvp471
Abstract: Let $G$ and $S$ be the location and the maximal value of a stable Lévy process $X$ on an interval $[0,a]$. It is shown that the dimensionless $S/G^h$, where h is the self-similarity parameter of $X$, is independent of $G$. This fact allows us to analyze $G$ for the trajectories of $X$ with high and low maxima.
Keywords: extremal values, Lévy processes, self-similar processes.
Received: 15.09.1999
English version:
Theory of Probability and its Applications, 2001, Volume 45, Issue 2, Pages 343–349
DOI: https://doi.org/10.1137/S0040585X97978294
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. M. Molchan, “On a maximum of stable Lévy processes”, Teor. Veroyatnost. i Primenen., 45:2 (2000), 380–386; Theory Probab. Appl., 45:2 (2001), 343–349
Citation in format AMSBIB
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\paper On a maximum of stable L\'evy processes
\jour Teor. Veroyatnost. i Primenen.
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\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 2
\pages 343--349
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  • https://www.mathnet.ru/eng/tvp/v45/i2/p380
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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