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dc.contributor.authorGrebenkov, D. S.
dc.contributor.authorSposini, V.
dc.contributor.authorMetzler, R.
dc.contributor.authorOshanin, G.
dc.contributor.authorSeno, F.
dc.date.accessioned2021-05-07T12:46:19Z
dc.date.available2021-05-07T12:46:19Z
dc.date.issued2021-02-09
dc.identifier.issn1367-2630
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1287
dc.description.abstractWe 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.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectAnomalous diffusionen_US
dc.subjectRandom diffusivity modelsen_US
dc.titleExact distributions of the maximum and range of random diffusivity processesen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.publisherversionhttps://iopscience.iop.org/article/10.1088/1367-2630/abd313/pdfen_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleNew Journal of Physicsen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España