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Properties of Kagi and Renko Moments for Homogeneous Diffusion Processes
M. A. Spiryaev M. V. Lomonosov Moscow State University
Abstract:
For a homogeneous diffusion process $(X_t)_{t\geqslant 0}$, we consider problems related to the distribution of the stopping times
\begin{gather*}
\gamma_{\max}=\inf\Bigl\{t\ge 0:\sup_{s\le t}X_s-X_t \ge H\Bigr\},\qquad
\gamma_{\min}=\inf \Bigl\{t\ge 0: X_t-\inf_{s\le t}X_s \ge H \Bigr\},
\\
\kappa_0=\inf\Bigl\{t\ge 0:\sup_{s\le t}X_s-\inf_{s\le t}X_s \ge H\Bigr\}.
\end{gather*}
The results obtained are used to construct an inductive procedure allowing us to find the distribution of the increments of the process $X$ between two adjacent kagi and renko instants of time.
Keywords:
homogeneous diffusion process, Brownian motion, stopping time, kagi instant of time, renko instant of time, Laplace transform.
Received: 14.03.2011
Citation:
M. A. Spiryaev, “Properties of Kagi and Renko Moments for Homogeneous Diffusion Processes”, Mat. Zametki, 91:2 (2012), 270–284; Math. Notes, 91:2 (2012), 259–271
Linking options:
https://www.mathnet.ru/eng/mzm9077https://doi.org/10.4213/mzm9077 https://www.mathnet.ru/eng/mzm/v91/i2/p270
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Abstract page: | 374 | Full-text PDF : | 168 | References: | 45 | First page: | 21 |
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