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 2021-05-07T12:46:19Z dc.date.available 2021-05-07T12:46:19Z dc.date.issued 2021-02-09 dc.identifier.issn 1367-2630 dc.identifier.uri http://hdl.handle.net/20.500.11824/1287 dc.description.abstract We study the extremal properties of a stochastic process $x_t$ defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$, in which $\xi_t$ is a Gaussian white noise with zero mean and $D_t$ is a stochastic 'diffusivity', defined as a functional of independent Brownian motion $B_t$. We focus on three choices for the random diffusivity $D_t$: cut-off Brownian motion, $D_t \sim \Theta(B_t)$, where $\Theta(x)$ is the Heaviside step function; geometric Brownian motion, $D_t \sim exp(−B_t)$; and a superdiffusive process based on squared Brownian motion, ${D}_{t}\sim {B}_{t}^{2}$. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process $x_t$ on the time interval $t \in (0, T)$. We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity ($D_t = D_0$) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process. en_US 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 Anomalous diffusion en_US dc.subject Random diffusivity models en_US dc.title Exact distributions of the maximum and range of random diffusivity processes en_US dc.type info:eu-repo/semantics/article en_US dc.relation.publisherversion https://iopscience.iop.org/article/10.1088/1367-2630/abd313/pdf 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 New Journal of Physics en_US
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