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Seminar on Probability Theory and Mathematical Statistics
September 16, 2011 18:00, St. Petersburg, PDMI, room 311 (nab. r. Fontanki, 27)
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On locally constant self-similar processes
Yu. A. Davydov |
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This page: | 178 |
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Abstract:
Let $X=\{X(t);\,t\in R_+\}$ be a real self-similar process. We say that $X$ is locally constant (LC) if for each $t>0$ with probability $1$ there exist $\epsilon>0$ such that $X(s)=X(t)$ for all $s\in(t-\epsilon,t+\epsilon)$.
We show that if a LC process $X$ is obtained by Lamperti transformation from an ergodic stationary process, then the law of $X(t)$ is absolutely continuous. Different examples are discussed. Special attention is payed to FBM and a large class of max-stable processes.
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