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- W3010062893 abstract "We study the question on whether or not the property of lack of memory that is valid for the geometrical and exponential distributions remains valid for hitting functionals in the case of upper almost semicontinuous processes defined on a Markov chain. If a boundary is attainable and the state of the environment is known at the moment when this boundary is attained, then the lack of memory holds only for an overshoot over a boundary $xge 0$ and the distribution of the overshoot does not depend on the overshoot moment as well as on $x$. The distribution of an undershoot for a boundary $x$ is determined via the distribution of the undershoot for a zero boundary. A similar property is proved for a jump crossing a boundary $x$." @default.
- W3010062893 created "2020-03-13" @default.
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- W3010062893 date "2020-02-27" @default.
- W3010062893 modified "2023-10-16" @default.
- W3010062893 title "On the lack of memory for distributions of overshoot functionals in the case of upper almost semicontinuous processes defined on a Markov chain" @default.
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- W3010062893 doi "https://doi.org/10.1090/tpms/1081" @default.
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