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- W4286898247 abstract "We describe the topology of superlevel sets of ($alpha$-stable) L'evy processes $X$ by introducing so-called stochastic $zeta$-functions, which are defined in terms of the widely used $text{Pers}_p$-functional in the theory of persistence modules. The latter share many of the properties commonly attributed to $zeta$-functions in analytic number theory, among others, we show that for $alpha$-stable processes, these (tail) $zeta$-functions always admit a meromorphic extension to the entire complex plane with a single pole at $alpha$, of known residue and that the analytic properties of these $zeta$-functions are related to the asymptotic expansion of a dual variable, which counts the number of variations of $X$ of size $geq varepsilon$. Finally, using these results, we devise a new statistical parameter test using the topology of these superlevel sets." @default.
- W4286898247 created "2022-07-25" @default.
- W4286898247 creator A5056812488 @default.
- W4286898247 date "2021-10-19" @default.
- W4286898247 modified "2023-09-28" @default.
- W4286898247 title "$zeta$-functions and the topology of superlevel sets of stochastic processes" @default.
- W4286898247 hasPublicationYear "2021" @default.
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