dc.contributor.author Grebenkov, D. S. dc.contributor.author Sposini, V. dc.contributor.author Metzler, R. dc.contributor.author Oshanin, G. dc.contributor.author Seno, F. dc.date.accessioned 2021-02-09T18:16:45Z dc.date.available 2021-02-09T18:16:45Z dc.date.issued 2021-01-04 dc.identifier.issn 1751-8121 dc.identifier.uri http://hdl.handle.net/20.500.11824/1250 dc.description.abstract We study the extremal properties of a stochastic process $x_t$ defined by en_US a Langevin equation $\dot{x}= \sqrt{2D_o V (B_t )} \xi_t$, where $\xi$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, and $V (B_t)$ is a stochastic "diffusivity" (noise strength), which itself is a functional of independent Brownian motion $B_t$. We derive exact, compact expressions in one and three dimensions for the probability density functions (PDFs) of the first passage time (FPT) $t$ from a fixed location $x_0$ to the origin for three different realisations of the stochastic diffusivity: a cut-off case $V (B_t) = \Theta(B_t)$ (Model I), where $\Theta(z)$ is the Heaviside theta function; a Geometric Brownian Motion $V (B_t) = exp(B_t)$ (Model II); and a case with $V (B_t) = B_t^2$ (Model III). We realise that, rather surprisingly, the FPT PDF has exactly the L\'evy-Smirnov form (specific for standard Brownian motion) for Model II, which concurrently exhibits a strongly anomalous diffusion. For Models I and III either the left or right tails (or both) have a different functional dependence on time as compared to the L\'evy-Smirnov density. In all cases, the PDFs are broad such that already the first moment does not exist. Similar results are obtained in three dimensions for the FPT PDF to an absorbing spherical target. dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject First-passage time distributions en_US dc.subject Random diffusivity models en_US dc.subject Anomalous diffusion en_US dc.title Exact first-passage time distributions for three random diffusivity models en_US dc.type info:eu-repo/semantics/article en_US dc.relation.publisherversion https://iopscience.iop.org/article/10.1088/1751-8121/abd42c en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Journal of Physics A: Mathematical and Theoretical en_US
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