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 Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 4, Pages 783–789 (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

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.

DOI: https://doi.org/10.4213/tvp134

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English version:
Theory of Probability and its Applications, 2006, 50:4, 694–700

Bibliographic databases:

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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