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- W1976500003 abstract "A Brownian motion is considered under the condition that it is stopped when attaining the level $(-varepsilon)$, $varepsilon>0$, provided that the level 1 is attained earlier than the level $(-varepsilon)$. It is proved that, as $varepsilon to 0$, this process converges in distribution in $C[0,+infty)$ to a stochastic process called a Brownian high jump. It is shown that the limiting process coincides in distribution with a piece of a Brownian trajectory between two of its sequential zeros such that the first moment of attaining level 1 is located between them. It is demonstrated that it is the Brownian high jump that is the limiting one in the invariance principle for the critical branching process in a random environment attaining a high level. Finite-dimensional distributions are found for the Brownian high jump, and the distributions of some of its functionals are calculated." @default.
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- W1976500003 date "2011-01-01" @default.
- W1976500003 modified "2023-09-27" @default.
- W1976500003 title "Brownian High Jump" @default.
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- W1976500003 doi "https://doi.org/10.1137/s0040585x97984747" @default.
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