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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 4, Pages 783–789
DOI: https://doi.org/10.4213/tvp134 (Mi tvp134) 		 
Short Communications

Distribution of length and height of trends for Brownian motion with a drift

S. N. Lobanov

Steklov Mathematical Institute, Russian Academy of Sciences
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DOI: https://doi.org/10.4213/tvp134
Abstract: The concept of trend is one of the basic concepts in describing process behavior. There are at least several definitions of trends and often the notion of trend is used without making a precise definition. This work examines two definitions of trend, which are frequently used, and establishes the link between them. Moreover the description of distribution of trend height and length is given. Since Brownian motion is the benchmark model in financial mathematics these characteristics give the reference point with respect to which one should consider the empirical characteristics of trends.
Keywords: trend, trend length, trend height, Brownian motion with drift.
Received: 16.10.2005
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 4, Pages 694–700
DOI: https://doi.org/10.1137/S0040585X97982086
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. N. Lobanov, “Distribution of length and height of trends for Brownian motion with a drift”, Teor. Veroyatnost. i Primenen., 50:4 (2005), 783–789; Theory Probab. Appl., 50:4 (2006), 694–700
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v50/i4/p783
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    References:66
     
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